Properties

Label 392784o
Number of curves $1$
Conductor $392784$
CM no
Rank $1$

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

Elliptic curves in class 392784o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.o1 392784o1 \([0, -1, 0, -277404696, -1775819982096]\) \(4899107302599545932681/7787470676557824\) \(3752706611717535480938496\) \([]\) \(130056192\) \(3.6132\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 392784o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 392784o do not have complex multiplication.

Modular form 392784.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 2 q^{11} - 6 q^{13} + q^{15} + 8 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display