Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 75712.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.o1 75712n1 \([0, 1, 0, -225, -1793]\) \(-114244/49\) \(-542703616\) \([]\) \(30720\) \(0.38357\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75712.o1 has rank \(1\).

Complex multiplication

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

Modular form 75712.2.a.o

sage: E.q_eigenform(10)
 
\(q - 2q^{3} + q^{5} - q^{7} + q^{9} + 2q^{11} - 2q^{15} - 3q^{17} - 8q^{19} + O(q^{20})\)  Toggle raw display