Properties

Label 458640.p
Number of curves $1$
Conductor $458640$
CM no
Rank $1$

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

Elliptic curves in class 458640.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
458640.p1 458640p1 \([0, 0, 0, -1383123, -3503386222]\) \(-832972004929/14611251200\) \(-5132903786006917939200\) \([]\) \(28200960\) \(2.8470\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 458640.p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 458640.p do not have complex multiplication.

Modular form 458640.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{5} - 5 q^{11} + q^{13} + 2 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display