Properties

Label 388416.ic
Number of curves $1$
Conductor $388416$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ic1")
 
E.isogeny_class()
 

Elliptic curves in class 388416.ic

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.ic1 388416ic1 \([0, 1, 0, -40765569, 102648409983]\) \(-1184052061112257/34349180544\) \(-217345088677283767517184\) \([]\) \(46448640\) \(3.2572\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388416.ic1 has rank \(1\).

Complex multiplication

The elliptic curves in class 388416.ic do not have complex multiplication.

Modular form 388416.2.a.ic

sage: E.q_eigenform(10)
 
\(q + q^{3} + 3 q^{5} - q^{7} + q^{9} - q^{11} - q^{13} + 3 q^{15} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display