Properties

Label 78400.r
Number of curves $1$
Conductor $78400$
CM no
Rank $0$

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

Elliptic curves in class 78400.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.r1 78400dh1 \([0, 0, 0, -700, 7000]\) \(48384\) \(784000000\) \([]\) \(53760\) \(0.49693\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 78400.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 78400.r do not have complex multiplication.

Modular form 78400.2.a.r

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} + 6 q^{9} + q^{11} - 2 q^{13} + 3 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display