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SageMath
E = EllipticCurve("il1")
E.isogeny_class()
Elliptic curves in class 485100.il
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.il1 | 485100il2 | \([0, 0, 0, -385900200, 2917834258500]\) | \(-1647408715474378752/3025\) | \(-11670050700000000\) | \([]\) | \(46282752\) | \(3.2295\) | \(\Gamma_0(N)\)-optimal* |
485100.il2 | 485100il1 | \([0, 0, 0, -4750200, 4027208500]\) | \(-2239956387422208/27680640625\) | \(-146485950187500000000\) | \([]\) | \(15427584\) | \(2.6802\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485100.il have rank \(0\).
Complex multiplication
The elliptic curves in class 485100.il do not have complex multiplication.Modular form 485100.2.a.il
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.