Properties

Label 56350.w
Number of curves $1$
Conductor $56350$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 56350.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.w1 56350p1 \([1, 1, 0, -29075, 1902125]\) \(-811543975/2944\) \(-9861250000000\) \([]\) \(188160\) \(1.3544\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 56350.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 56350.w do not have complex multiplication.

Modular form 56350.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - q^{8} + q^{9} + 2 q^{12} + 5 q^{13} + q^{16} + 7 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display