Properties

Label 7098.r
Number of curves $1$
Conductor $7098$
CM no
Rank $1$

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

Elliptic curves in class 7098.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.r1 7098v1 \([1, 1, 1, -49, 47]\) \(77086633/32928\) \(5564832\) \([]\) \(1440\) \(-0.0091272\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7098.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 7098.r do not have complex multiplication.

Modular form 7098.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - 2 q^{10} + q^{11} - q^{12} + q^{14} + 2 q^{15} + q^{16} - q^{17} + q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display