Properties

Label 1470.r
Number of curves $1$
Conductor $1470$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 1470.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1470.r1 1470r1 \([1, 0, 0, -1765, -29023]\) \(-105484561/1440\) \(-8301313440\) \([]\) \(1680\) \(0.71017\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1470.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1470.r do not have complex multiplication.

Modular form 1470.2.a.r

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