Properties

Label 49725.l
Number of curves $1$
Conductor $49725$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 49725.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
49725.l1 49725a1 \([0, 0, 1, -180450, 47736156]\) \(-1540318675894272/1442042265625\) \(-608361580810546875\) \([]\) \(510720\) \(2.1089\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 49725.l1 has rank \(1\).

Complex multiplication

The elliptic curves in class 49725.l do not have complex multiplication.

Modular form 49725.2.a.l

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