Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7098.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.o1 7098m1 \([1, 0, 1, -7838393, 9140787164]\) \(-5022437771811277/497757560832\) \(-5278469741748953358336\) \([]\) \(535392\) \(2.9087\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 7098.o1 has rank \(1\).

Complex multiplication

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

Modular form 7098.2.a.o

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