Properties

Label 7728.e
Number of curves $1$
Conductor $7728$
CM no
Rank $0$

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

Elliptic curves in class 7728.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7728.e1 7728g1 \([0, -1, 0, 27, -51]\) \(512000/483\) \(-1978368\) \([]\) \(800\) \(-0.10468\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7728.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 7728.e do not have complex multiplication.

Modular form 7728.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} - q^{11} + 2 q^{13} + 4 q^{17} + 3 q^{19} + O(q^{20})\)  Toggle raw display