Properties

Label 388416p
Number of curves $1$
Conductor $388416$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 388416p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.p1 388416p1 \([0, -1, 0, -48937, -4870121]\) \(-8390176768/1821771\) \(-2814279885740736\) \([]\) \(2580480\) \(1.6854\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388416p1 has rank \(1\).

Complex multiplication

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

Modular form 388416.2.a.p

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