Properties

Label 75150.r
Number of curves $1$
Conductor $75150$
CM no
Rank $1$

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

Elliptic curves in class 75150.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75150.r1 75150m1 \([1, -1, 0, -734292, -242351384]\) \(-3843995587427449/6390046584\) \(-72786624370875000\) \([]\) \(1128960\) \(2.1314\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75150.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75150.r do not have complex multiplication.

Modular form 75150.2.a.r

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