Properties

Label 249714g
Number of curves $1$
Conductor $249714$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 249714g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249714.g1 249714g1 \([1, -1, 1, -104, -709]\) \(-169112377/221968\) \(-161814672\) \([]\) \(139776\) \(0.26808\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 249714g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 249714g do not have complex multiplication.

Modular form 249714.2.a.g

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