Properties

Label 425.c
Number of curves $1$
Conductor $425$
CM no
Rank $1$

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

Elliptic curves in class 425.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
425.c1 425b1 \([1, 1, 0, -75, 250]\) \(-121945/17\) \(-6640625\) \([]\) \(60\) \(0.040527\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 425.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 425.c do not have complex multiplication.

Modular form 425.2.a.c

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