Properties

Label 493680i
Number of curves $1$
Conductor $493680$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 493680i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
493680.i1 493680i1 \([0, -1, 0, -62476, 6730495]\) \(-951468070144/135517455\) \(-3841239009556080\) \([]\) \(2970240\) \(1.7213\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 493680i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 493680i do not have complex multiplication.

Modular form 493680.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 3 q^{7} + q^{9} + 2 q^{13} + q^{15} + q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display