Properties

Label 56350w
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 56350w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.t1 56350w1 \([1, 0, 1, -100721, 12345988]\) \(-156813434813/753664\) \(-543090372608000\) \([]\) \(352800\) \(1.6764\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 56350.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} - 2 q^{9} - 4 q^{11} + q^{12} + q^{13} + q^{16} + 7 q^{17} + 2 q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display