Properties

Label 13725c
Number of curves $1$
Conductor $13725$
CM no
Rank $0$

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

Elliptic curves in class 13725c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13725.a1 13725c1 \([1, -1, 1, -455, -3828]\) \(-912673/61\) \(-694828125\) \([]\) \(5184\) \(0.44857\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 13725c1 has rank \(0\).

Complex multiplication

The elliptic curves in class 13725c do not have complex multiplication.

Modular form 13725.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{7} + 3 q^{8} + 5 q^{11} - q^{13} + q^{14} - q^{16} + 4 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display