Properties

Label 2175.f
Number of curves $1$
Conductor $2175$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 2175.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2175.f1 2175g1 \([0, 1, 1, -153, 749]\) \(-15947530240/1839267\) \(-45981675\) \([]\) \(336\) \(0.20672\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2175.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 2175.f do not have complex multiplication.

Modular form 2175.2.a.f

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