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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 412224.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
412224.c1 | 412224c2 | \([0, -1, 0, -2585, 50841]\) | \(466566337216/6550497\) | \(26830835712\) | \([2]\) | \(737280\) | \(0.80611\) | \(\Gamma_0(N)\)-optimal* |
412224.c2 | 412224c1 | \([0, -1, 0, -20, 2106]\) | \(-14526784/29738097\) | \(-1903238208\) | \([2]\) | \(368640\) | \(0.45954\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 412224.c have rank \(1\).
Complex multiplication
The elliptic curves in class 412224.c do not have complex multiplication.Modular form 412224.2.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.