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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 254100.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.v1 | 254100v2 | \([0, -1, 0, -1592158, -774905063]\) | \(-121947169848064/397065375\) | \(-1453358538843750000\) | \([]\) | \(5598720\) | \(2.3509\) | |
254100.v2 | 254100v1 | \([0, -1, 0, 41342, -5526563]\) | \(2134896896/4822335\) | \(-17650951683750000\) | \([]\) | \(1866240\) | \(1.8016\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254100.v have rank \(1\).
Complex multiplication
The elliptic curves in class 254100.v do not have complex multiplication.Modular form 254100.2.a.v
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.