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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 227430eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227430.y1 | 227430eq1 | \([1, -1, 0, -4243860, -3067729200]\) | \(1690513270434786979/164670952320000\) | \(823389507170939520000\) | \([2]\) | \(12902400\) | \(2.7505\) | \(\Gamma_0(N)\)-optimal |
| 227430.y2 | 227430eq2 | \([1, -1, 0, 5140620, -14740145424]\) | \(3004566620369762141/20506979587500000\) | \(-102539224910192962500000\) | \([2]\) | \(25804800\) | \(3.0971\) |
Rank
sage: E.rank()
The elliptic curves in class 227430eq have rank \(1\).
Complex multiplication
The elliptic curves in class 227430eq do not have complex multiplication.Modular form 227430.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
