Properties

Label 7605.u
Number of curves $1$
Conductor $7605$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 7605.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7605.u1 7605s1 \([0, 0, 1, -289497, -61563785]\) \(-762549907456/24024195\) \(-84534986269297395\) \([]\) \(112896\) \(2.0243\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7605.u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 7605.u do not have complex multiplication.

Modular form 7605.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{4} + q^{5} - 3 q^{7} + 2 q^{10} - q^{11} - 6 q^{14} - 4 q^{16} + q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display