Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.dc1 75712ci1 \([0, 0, 0, 35828, 4394000]\) \(4019679/8918\) \(-11284115006947328\) \([]\) \(1161216\) \(1.7643\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.dc1 has rank \(0\).

Complex multiplication

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

Modular form 75712.2.a.dc

sage: E.q_eigenform(10)
 
\(q + 3q^{3} - 4q^{5} - q^{7} + 6q^{9} - q^{11} - 12q^{15} + 6q^{19} + O(q^{20})\)  Toggle raw display