Properties

Label 70602.o
Number of curves $1$
Conductor $70602$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Elliptic curves in class 70602.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
70602.o1 70602w1 \([1, 1, 1, -831521814, 21712415552787]\) \(-194218207880195897/509703742291968\) \(-166867797119385472523198005248\) \([]\) \(89622720\) \(4.2948\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 70602.o1 has rank \(1\).

Complex multiplication

The elliptic curves in class 70602.o do not have complex multiplication.

Modular form 70602.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - 2 q^{10} - 5 q^{11} - q^{12} - 2 q^{13} + q^{14} + 2 q^{15} + q^{16} + 2 q^{17} + q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display