Properties

Label 71478.d
Number of curves $1$
Conductor $71478$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 71478.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
71478.d1 71478p1 \([1, -1, 0, -1008, -13824]\) \(-430638553/76032\) \(-20009265408\) \([]\) \(55296\) \(0.70229\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 71478.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 71478.d do not have complex multiplication.

Modular form 71478.2.a.d

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