Properties

Label 225318.r
Number of curves $1$
Conductor $225318$
CM no
Rank $1$

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

Elliptic curves in class 225318.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
225318.r1 225318h1 \([1, 1, 1, -1491072285185, 700802714776192661]\) \(-15397029525197722850243627281/15665817798\) \(-373023278379095479822278\) \([]\) \(4152844800\) \(5.1945\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 225318.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 225318.r do not have complex multiplication.

Modular form 225318.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 4 q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} - 4 q^{10} - 6 q^{11} - q^{12} + 4 q^{13} + 2 q^{14} + 4 q^{15} + q^{16} - q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display