Properties

Label 37575c
Number of curves $1$
Conductor $37575$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 37575c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37575.d1 37575c1 \([1, -1, 0, -12807, -556524]\) \(-2549455723781/9861183\) \(-898600300875\) \([]\) \(74240\) \(1.1520\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 37575c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 37575c do not have complex multiplication.

Modular form 37575.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 4 q^{7} - 3 q^{8} - q^{11} - 5 q^{13} - 4 q^{14} - q^{16} + 3 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display