Properties

Label 42384.a
Number of curves $1$
Conductor $42384$
CM no
Rank $3$

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

Elliptic curves in class 42384.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42384.a1 42384a1 \([0, -1, 0, -80, 336]\) \(-55990084/7947\) \(-8137728\) \([]\) \(23680\) \(0.057013\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42384.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 42384.a do not have complex multiplication.

Modular form 42384.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{5} - 4 q^{7} + q^{9} - 6 q^{11} - 3 q^{13} + 4 q^{15} - 7 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display