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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 400710p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400710.p2 | 400710p1 | \([1, 0, 1, -413714, 161696036]\) | \(-166456688365729/143856000000\) | \(-6767832257136000000\) | \([2]\) | \(7862400\) | \(2.3106\) | \(\Gamma_0(N)\)-optimal* |
400710.p1 | 400710p2 | \([1, 0, 1, -7633714, 8115248036]\) | \(1045706191321645729/323352324000\) | \(15212394955977444000\) | \([2]\) | \(15724800\) | \(2.6572\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 400710p have rank \(0\).
Complex multiplication
The elliptic curves in class 400710p do not have complex multiplication.Modular form 400710.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.