Properties

Label 5175t
Number of curves $1$
Conductor $5175$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 5175t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5175.z1 5175t1 \([0, 0, 1, -165, -819]\) \(-5451776/23\) \(-2095875\) \([]\) \(1344\) \(0.067596\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5175t1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5175t do not have complex multiplication.

Modular form 5175.2.a.t

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