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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 40310.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40310.p1 | 40310bd2 | \([1, -1, 1, -310196027862, -66496985128639551]\) | \(-3300900313422115945972159074168895576881/2907378668445199100\) | \(-2907378668445199100\) | \([]\) | \(206524416\) | \(4.7234\) | |
40310.p2 | 40310bd1 | \([1, -1, 1, -99013362, -835939931151]\) | \(-107350761560343751123953328881/239773280695100000000000000\) | \(-239773280695100000000000000\) | \([7]\) | \(29503488\) | \(3.7504\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40310.p have rank \(0\).
Complex multiplication
The elliptic curves in class 40310.p do not have complex multiplication.Modular form 40310.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.