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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 51870.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51870.a1 | 51870d1 | \([1, 1, 0, -259143312263, -52067329167215883]\) | \(-1924614389270758801170113620446515123449/57368590462870627697502749640000000\) | \(-57368590462870627697502749640000000\) | \([]\) | \(811399680\) | \(5.4478\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51870.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51870.a do not have complex multiplication.Modular form 51870.2.a.a
sage: E.q_eigenform(10)