Properties

Label 80850.o
Number of curves $1$
Conductor $80850$
CM no
Rank $1$

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

Elliptic curves in class 80850.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80850.o1 80850c1 \([1, 1, 0, -888757125, 11274931162125]\) \(-861923363555648023441/110929177533556800\) \(-9991947399603527721825000000\) \([]\) \(69189120\) \(4.1061\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 80850.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 80850.o do not have complex multiplication.

Modular form 80850.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - q^{11} - q^{12} + 4 q^{13} + q^{16} - 7 q^{17} - q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display