Properties

Label 289728.er
Number of curves $1$
Conductor $289728$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("er1")
 
E.isogeny_class()
 

Elliptic curves in class 289728.er

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289728.er1 289728er1 \([0, 0, 0, -468, 4320]\) \(-3796416/503\) \(-1501949952\) \([]\) \(261632\) \(0.49360\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 289728.er1 has rank \(0\).

Complex multiplication

The elliptic curves in class 289728.er do not have complex multiplication.

Modular form 289728.2.a.er

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} + 3 q^{7} - 3 q^{11} - 7 q^{13} + 2 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display