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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 10192.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10192.j1 | 10192w1 | \([0, -1, 0, -3544, 216560]\) | \(-29791/104\) | \(-17189990924288\) | \([]\) | \(16128\) | \(1.2256\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10192.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10192.j do not have complex multiplication.Modular form 10192.2.a.j
sage: E.q_eigenform(10)