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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 38962.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38962.p1 | 38962j2 | \([1, 1, 0, -1696, 21894]\) | \(304821217/51842\) | \(91841265362\) | \([2]\) | \(51840\) | \(0.82426\) | |
38962.p2 | 38962j1 | \([1, 1, 0, -486, -4000]\) | \(7189057/644\) | \(1140885284\) | \([2]\) | \(25920\) | \(0.47768\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38962.p have rank \(1\).
Complex multiplication
The elliptic curves in class 38962.p do not have complex multiplication.Modular form 38962.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.