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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 78400.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.cn1 | 78400cv2 | \([0, 1, 0, -1905633, 1011860863]\) | \(544737993463/20000\) | \(28098560000000000\) | \([2]\) | \(1474560\) | \(2.2438\) | |
78400.cn2 | 78400cv1 | \([0, 1, 0, -113633, 17300863]\) | \(-115501303/25600\) | \(-35966156800000000\) | \([2]\) | \(737280\) | \(1.8972\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78400.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 78400.cn do not have complex multiplication.Modular form 78400.2.a.cn
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.