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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2070.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2070.c1 | 2070e2 | \([1, -1, 0, -35325, 2564325]\) | \(6687281588245201/165600\) | \(120722400\) | \([2]\) | \(3840\) | \(1.0692\) | |
2070.c2 | 2070e1 | \([1, -1, 0, -2205, 40581]\) | \(-1626794704081/8125440\) | \(-5923445760\) | \([2]\) | \(1920\) | \(0.72264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2070.c have rank \(1\).
Complex multiplication
The elliptic curves in class 2070.c do not have complex multiplication.Modular form 2070.2.a.c
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.