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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 41616.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41616.cn1 | 41616cn2 | \([0, 0, 0, -2469216, -1494259472]\) | \(-23100424192/14739\) | \(-1062304505442054144\) | \([]\) | \(995328\) | \(2.3998\) | |
41616.cn2 | 41616cn1 | \([0, 0, 0, 27744, -8568272]\) | \(32768/459\) | \(-33082147228299264\) | \([]\) | \(331776\) | \(1.8505\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41616.cn have rank \(1\).
Complex multiplication
The elliptic curves in class 41616.cn do not have complex multiplication.Modular form 41616.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.