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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 51600.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.bt1 | 51600n1 | \([0, -1, 0, 137592, -110552688]\) | \(9002230481662/170068359375\) | \(-5442187500000000000\) | \([]\) | \(1013760\) | \(2.2755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51600.bt1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51600.bt do not have complex multiplication.Modular form 51600.2.a.bt
sage: E.q_eigenform(10)