Properties

Label 388416.o
Number of curves $1$
Conductor $388416$
CM no
Rank $1$

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

Elliptic curves in class 388416.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.o1 388416o1 \([0, -1, 0, -102458977, -399831382559]\) \(-130098552670514/257298363\) \(-235254706373180664446976\) \([]\) \(59222016\) \(3.3726\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388416.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 388416.o do not have complex multiplication.

Modular form 388416.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{7} + q^{9} + 3 q^{11} - 2 q^{13} + 3 q^{15} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display