Properties

Label 700.e
Number of curves $1$
Conductor $700$
CM no
Rank $1$

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

Elliptic curves in class 700.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
700.e1 700f1 \([0, 0, 0, -125, 625]\) \(-34560/7\) \(-43750000\) \([]\) \(180\) \(0.18864\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 700.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 700.e do not have complex multiplication.

Modular form 700.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3 q^{9} - 5 q^{11} + 6 q^{13} - 4 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display