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SageMath
E = EllipticCurve("ho1")
E.isogeny_class()
Elliptic curves in class 493680.ho
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.ho1 | 493680ho1 | \([0, 1, 0, -8213520, 9289443348]\) | \(-8444922396903721/253364474880\) | \(-1838492149689907937280\) | \([]\) | \(29030400\) | \(2.8583\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 493680.ho1 has rank \(0\).
Complex multiplication
The elliptic curves in class 493680.ho do not have complex multiplication.Modular form 493680.2.a.ho
sage: E.q_eigenform(10)