Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7728.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7728.r1 7728t1 \([0, 1, 0, -253, -7705]\) \(-7023616000/93934323\) \(-24047186688\) \([]\) \(7200\) \(0.67356\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7728.r1 has rank \(1\).

Complex multiplication

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

Modular form 7728.2.a.r

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