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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 41895.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41895.cb1 | 41895by2 | \([0, 0, 1, -7347207, -10067773473]\) | \(-511416541770305536/214587319023035\) | \(-18404321968395221597235\) | \([]\) | \(4320000\) | \(2.9802\) | |
41895.cb2 | 41895by1 | \([0, 0, 1, -92757, 62309637]\) | \(-1029077364736/18960396875\) | \(-1626159692589271875\) | \([]\) | \(864000\) | \(2.1755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41895.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 41895.cb do not have complex multiplication.Modular form 41895.2.a.cb
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.