Properties

Label 4056.c
Number of curves $1$
Conductor $4056$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 4056.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4056.c1 4056b1 \([0, -1, 0, -2929, -70955]\) \(-13312/3\) \(-626481193728\) \([]\) \(6240\) \(0.98371\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4056.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4056.c do not have complex multiplication.

Modular form 4056.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{7} + q^{9} - 6 q^{11} + 2 q^{15} + 8 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display