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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 3822.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3822.j1 | 3822m3 | \([1, 0, 1, -1016237, -394396936]\) | \(986551739719628473/111045168\) | \(13064352970032\) | \([2]\) | \(46080\) | \(1.9410\) | |
3822.j2 | 3822m4 | \([1, 0, 1, -114637, 5057336]\) | \(1416134368422073/725251155408\) | \(85325073182595792\) | \([2]\) | \(46080\) | \(1.9410\) | |
3822.j3 | 3822m2 | \([1, 0, 1, -63677, -6133480]\) | \(242702053576633/2554695936\) | \(300557422174464\) | \([2, 2]\) | \(23040\) | \(1.5945\) | |
3822.j4 | 3822m1 | \([1, 0, 1, -957, -237800]\) | \(-822656953/207028224\) | \(-24356663525376\) | \([2]\) | \(11520\) | \(1.2479\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3822.j have rank \(1\).
Complex multiplication
The elliptic curves in class 3822.j do not have complex multiplication.Modular form 3822.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.