Properties

Label 388815dk
Number of curves $1$
Conductor $388815$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("dk1")
 
E.isogeny_class()
 

Elliptic curves in class 388815dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388815.dk1 388815dk1 \([0, -1, 1, -317653590, 2857020553631]\) \(-2476357085090396229632/1030161895751953125\) \(-1474610187797703094482421875\) \([]\) \(330448896\) \(3.9213\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 388815dk1 has rank \(2\).

Complex multiplication

The elliptic curves in class 388815dk do not have complex multiplication.

Modular form 388815.2.a.dk

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