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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 38962b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38962.n2 | 38962b1 | \([1, 0, 1, 2659, 7984]\) | \(1174241375/694232\) | \(-1229874336152\) | \([]\) | \(51840\) | \(1.0092\) | \(\Gamma_0(N)\)-optimal |
38962.n1 | 38962b2 | \([1, 0, 1, -39691, 3189316]\) | \(-3903264618625/226719878\) | \(-401648093789558\) | \([]\) | \(155520\) | \(1.5585\) |
Rank
sage: E.rank()
The elliptic curves in class 38962b have rank \(0\).
Complex multiplication
The elliptic curves in class 38962b do not have complex multiplication.Modular form 38962.2.a.b
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.