Properties

Label 9075.e
Number of curves $1$
Conductor $9075$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 9075.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9075.e1 9075c1 \([1, 1, 1, -17608, -1059574]\) \(-10241915/2187\) \(-128920790005425\) \([]\) \(22176\) \(1.4288\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 9075.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 9075.e do not have complex multiplication.

Modular form 9075.2.a.e

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