Properties

Label 40425.r
Number of curves $1$
Conductor $40425$
CM no
Rank $1$

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

Elliptic curves in class 40425.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40425.r1 40425ba1 \([1, 1, 1, -117013, -15900844]\) \(-78683185/2673\) \(-6019262919140625\) \([]\) \(277200\) \(1.8016\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 40425.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 40425.r do not have complex multiplication.

Modular form 40425.2.a.r

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