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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 250470v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.v2 | 250470v1 | \([1, -1, 0, 40815, 50413941]\) | \(5822285399/853875000\) | \(-1102752212029875000\) | \([]\) | \(3317760\) | \(2.1413\) | \(\Gamma_0(N)\)-optimal |
250470.v1 | 250470v2 | \([1, -1, 0, -367560, -1366075584]\) | \(-4252315368601/621860236800\) | \(-803112577021955059200\) | \([]\) | \(9953280\) | \(2.6906\) |
Rank
sage: E.rank()
The elliptic curves in class 250470v have rank \(2\).
Complex multiplication
The elliptic curves in class 250470v do not have complex multiplication.Modular form 250470.2.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 Cremona 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 Cremona labels.