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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 35280eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.cw1 | 35280eq1 | \([0, 0, 0, -439383, -112169918]\) | \(-177953104/125\) | \(-6589582608672000\) | \([]\) | \(362880\) | \(1.9716\) | \(\Gamma_0(N)\)-optimal |
| 35280.cw2 | 35280eq2 | \([0, 0, 0, 424977, -476411222]\) | \(161017136/1953125\) | \(-102962228260500000000\) | \([]\) | \(1088640\) | \(2.5210\) |
Rank
sage: E.rank()
The elliptic curves in class 35280eq have rank \(0\).
Complex multiplication
The elliptic curves in class 35280eq do not have complex multiplication.Modular form 35280.2.a.eq
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.
