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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 95370.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95370.j1 | 95370c8 | \([1, 1, 0, -58157343448, -5398298602443968]\) | \(901247067798311192691198986281/552431869440\) | \(13334362366406991360\) | \([2]\) | \(191102976\) | \(4.3774\) | |
95370.j2 | 95370c7 | \([1, 1, 0, -3659249368, -83158963742912]\) | \(224494757451893010998773801/6152490825146276160000\) | \(148506171813835175905055040000\) | \([2]\) | \(191102976\) | \(4.3774\) | |
95370.j3 | 95370c6 | \([1, 1, 0, -3634834648, -84349518266048]\) | \(220031146443748723000125481/172266701724057600\) | \(4158099399266859279974400\) | \([2, 2]\) | \(95551488\) | \(4.0308\) | |
95370.j4 | 95370c5 | \([1, 1, 0, -718138273, -7402169105123]\) | \(1696892787277117093383481/1440538624914939000\) | \(34771100456049459243291000\) | \([2]\) | \(63700992\) | \(3.8281\) | |
95370.j5 | 95370c4 | \([1, 1, 0, -470314993, 3883691455213]\) | \(476646772170172569823801/5862293314453125000\) | \(141501509375851001953125000\) | \([2]\) | \(63700992\) | \(3.8281\) | |
95370.j6 | 95370c3 | \([1, 1, 0, -225651928, -1336600870592]\) | \(-52643812360427830814761/1504091705903677440\) | \(-36305117333577721561743360\) | \([2]\) | \(47775744\) | \(3.6842\) | |
95370.j7 | 95370c2 | \([1, 1, 0, -54883273, -60334208123]\) | \(757443433548897303481/373234243041000000\) | \(9008967294564907329000000\) | \([2, 2]\) | \(31850496\) | \(3.4815\) | |
95370.j8 | 95370c1 | \([1, 1, 0, 12534647, -7222370747]\) | \(9023321954633914439/6156756739584000\) | \(-148609140617923831296000\) | \([2]\) | \(15925248\) | \(3.1349\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95370.j have rank \(1\).
Complex multiplication
The elliptic curves in class 95370.j do not have complex multiplication.Modular form 95370.2.a.j
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.