Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 388416.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.s1 388416s1 \([0, -1, 0, -341507, 79802289]\) \(-14008675513670144/617773369563\) \(-194247716138433216\) \([]\) \(5447680\) \(2.0824\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388416.s1 has rank \(1\).

Complex multiplication

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

Modular form 388416.2.a.s

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