Properties

Label 493680.ho
Number of curves $1$
Conductor $493680$
CM no
Rank $0$

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Show commands: 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)
 
\(q + q^{3} + q^{5} + 3 q^{7} + q^{9} + q^{13} + q^{15} + q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display