Properties

Label 5070.d
Number of curves $1$
Conductor $5070$
CM no
Rank $0$

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

Elliptic curves in class 5070.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.d1 5070f1 \([1, 1, 0, 6749688, 2824854336]\) \(41689615345255319/28343520000000\) \(-23120680005277920000000\) \([]\) \(528528\) \(2.9799\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5070.d1 has rank \(0\).

Complex multiplication

The elliptic curves in class 5070.d do not have complex multiplication.

Modular form 5070.2.a.d

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