Properties

Label 51870.a
Number of curves $1$
Conductor $51870$
CM no
Rank $0$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 51870.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51870.a1 51870d1 \([1, 1, 0, -259143312263, -52067329167215883]\) \(-1924614389270758801170113620446515123449/57368590462870627697502749640000000\) \(-57368590462870627697502749640000000\) \([]\) \(811399680\) \(5.4478\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51870.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 51870.a do not have complex multiplication.

Modular form 51870.2.a.a

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