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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 5712d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5712.l2 | 5712d1 | \([0, -1, 0, -6032, -1879920]\) | \(-23707171994692/1480419781911\) | \(-1515949856676864\) | \([2]\) | \(33792\) | \(1.5927\) | \(\Gamma_0(N)\)-optimal |
5712.l1 | 5712d2 | \([0, -1, 0, -268472, -53108208]\) | \(1044942448578893426/7759962920241\) | \(15892404060653568\) | \([2]\) | \(67584\) | \(1.9393\) |
Rank
sage: E.rank()
The elliptic curves in class 5712d have rank \(0\).
Complex multiplication
The elliptic curves in class 5712d do not have complex multiplication.Modular form 5712.2.a.d
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.