Properties

Label 249090.r
Number of curves $1$
Conductor $249090$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 249090.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
249090.r1 249090r1 \([1, 1, 0, -130855287, -603620175339]\) \(-14590451544283839961/822700800000000\) \(-13972390900681132800000000\) \([]\) \(76608000\) \(3.5821\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 249090.r1 has rank \(2\).

Complex multiplication

The elliptic curves in class 249090.r do not have complex multiplication.

Modular form 249090.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 3 q^{7} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} + 3 q^{14} - q^{15} + q^{16} - q^{18} + O(q^{20})\) Copy content Toggle raw display