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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 44616u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44616.t4 | 44616u1 | \([0, 1, 0, 113, 12650]\) | \(2048/891\) | \(-68810989104\) | \([2]\) | \(46080\) | \(0.75865\) | \(\Gamma_0(N)\)-optimal |
44616.t3 | 44616u2 | \([0, 1, 0, -7492, 240800]\) | \(37642192/1089\) | \(1345637120256\) | \([2, 2]\) | \(92160\) | \(1.1052\) | |
44616.t2 | 44616u3 | \([0, 1, 0, -17632, -562288]\) | \(122657188/43923\) | \(217096122067968\) | \([2]\) | \(184320\) | \(1.4518\) | |
44616.t1 | 44616u4 | \([0, 1, 0, -119032, 15767168]\) | \(37736227588/33\) | \(163107529728\) | \([2]\) | \(184320\) | \(1.4518\) |
Rank
sage: E.rank()
The elliptic curves in class 44616u have rank \(0\).
Complex multiplication
The elliptic curves in class 44616u do not have complex multiplication.Modular form 44616.2.a.u
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.