Properties

Label 418950.r
Number of curves $1$
Conductor $418950$
CM no
Rank $2$

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

Elliptic curves in class 418950.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
418950.r1 418950r1 \([1, -1, 0, -244617, 12180041]\) \(48317985/26068\) \(873340328995312500\) \([]\) \(6773760\) \(2.1337\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 418950.r1 has rank \(2\).

Complex multiplication

The elliptic curves in class 418950.r do not have complex multiplication.

Modular form 418950.2.a.r

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