Properties

Label 1300.e
Number of curves $1$
Conductor $1300$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 1300.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1300.e1 1300a1 \([0, 0, 0, 625, -6250]\) \(10800/13\) \(-32500000000\) \([]\) \(720\) \(0.70323\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1300.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1300.e do not have complex multiplication.

Modular form 1300.2.a.e

sage: E.q_eigenform(10)
 
\(q + 3 q^{7} - 3 q^{9} + 3 q^{11} - q^{13} + q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display