Properties

Label 457776p
Number of curves $1$
Conductor $457776$
CM no
Rank $1$

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

Elliptic curves in class 457776p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
457776.p1 457776p1 \([0, 0, 0, -10404, 530604]\) \(-27648/11\) \(-49551146447616\) \([]\) \(1032192\) \(1.3367\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 457776p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 457776p do not have complex multiplication.

Modular form 457776.2.a.p

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} - 2 q^{7} + q^{11} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display