Properties

Label 75712.d
Number of curves $1$
Conductor $75712$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.d1 75712bl1 \([0, 0, 0, -33807436, -75672026768]\) \(-19983597574473/3670016\) \(-784792236264400093184\) \([]\) \(11381760\) \(3.0122\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.d1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.d

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