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Properties

Label 451770ba
Number of curves $1$
Conductor $451770$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ba1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 451770ba1 has rank \(0\).

Complex multiplication

The elliptic curves in class 451770ba do not have complex multiplication.

Modular form 451770.2.a.ba

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

Elliptic curves in class 451770ba

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
451770.ba1 451770ba1 \([1, 0, 1, -4977713, 7958133956]\) \(-3883285783081/5542732800\) \(-19468735078574015308800\) \([]\) \(34525440\) \(2.9691\) \(\Gamma_0(N)\)-optimal