Properties

Label 7623.e
Number of curves $1$
Conductor $7623$
CM no
Rank $1$

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

Elliptic curves in class 7623.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7623.e1 7623h1 \([1, -1, 1, -3506603, 2534429868]\) \(-30515071121161/85766121\) \(-13402467969722268129\) \([]\) \(228096\) \(2.5425\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7623.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 7623.e do not have complex multiplication.

Modular form 7623.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} - q^{7} + 3 q^{8} + q^{10} - 5 q^{13} + q^{14} - q^{16} - 7 q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display