Properties

Label 250075.c
Number of curves $1$
Conductor $250075$
CM no
Rank $1$

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

Elliptic curves in class 250075.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
250075.c1 250075c1 \([1, 0, 1, 1299, 23423]\) \(15531437375/24017203\) \(-375268796875\) \([]\) \(282240\) \(0.90620\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 250075.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 250075.c do not have complex multiplication.

Modular form 250075.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} - 2 q^{6} + q^{7} - 3 q^{8} + q^{9} + 6 q^{11} + 2 q^{12} + 2 q^{13} + q^{14} - q^{16} + 4 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display