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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 7056.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7056.c1 | 7056ba2 | \([0, 0, 0, -17787, 902090]\) | \(3543122/49\) | \(8606801774592\) | \([2]\) | \(18432\) | \(1.2876\) | |
7056.c2 | 7056ba1 | \([0, 0, 0, -147, 37730]\) | \(-4/7\) | \(-614771555328\) | \([2]\) | \(9216\) | \(0.94102\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.c have rank \(1\).
Complex multiplication
The elliptic curves in class 7056.c do not have complex multiplication.Modular form 7056.2.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.