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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 247962.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
247962.v1 | 247962v2 | \([1, 1, 1, -2130514, -1196405665]\) | \(44308125149913793/61165323648\) | \(1476382219960931712\) | \([2]\) | \(8386560\) | \(2.3907\) | |
247962.v2 | 247962v1 | \([1, 1, 1, -95954, -29382049]\) | \(-4047806261953/13066420224\) | \(-315391619739795456\) | \([2]\) | \(4193280\) | \(2.0441\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 247962.v have rank \(0\).
Complex multiplication
The elliptic curves in class 247962.v do not have complex multiplication.Modular form 247962.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.