Properties

Label 19600ec
Number of curves $1$
Conductor $19600$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("ec1")
 
E.isogeny_class()
 

Elliptic curves in class 19600ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.dw1 19600ec1 \([0, 0, 0, -49000, 4287500]\) \(-221184/7\) \(-411771500000000\) \([]\) \(138240\) \(1.5805\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 19600ec1 has rank \(0\).

Complex multiplication

The elliptic curves in class 19600ec do not have complex multiplication.

Modular form 19600.2.a.ec

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + 6 q^{9} - 3 q^{11} - q^{13} + 5 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display