Properties

Label 75712.i
Number of curves $1$
Conductor $75712$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 75712.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.i1 75712da1 \([0, 1, 0, -901, -903837]\) \(-1024/4459\) \(-352628593967104\) \([]\) \(258048\) \(1.4703\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75712.i do not have complex multiplication.

Modular form 75712.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + q^{7} + q^{9} - 4 q^{11} + 2 q^{15} - 6 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display