Properties

Label 42264.a
Number of curves $1$
Conductor $42264$
CM no
Rank $3$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 42264.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42264.a1 42264a1 \([0, 0, 0, -252, 1620]\) \(-9483264/587\) \(-109548288\) \([]\) \(39168\) \(0.29696\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42264.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 42264.a do not have complex multiplication.

Modular form 42264.2.a.a

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} - 5 q^{7} - 6 q^{11} - 6 q^{13} - 5 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display