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Properties

Label 60690by
Number of curves $1$
Conductor $60690$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("by1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 60690by1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(7\)\(1 - T\)
\(17\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - T + 11 T^{2}\) 1.11.ab
\(13\) \( 1 + 5 T + 13 T^{2}\) 1.13.f
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 + 4 T + 29 T^{2}\) 1.29.e
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 60690by do not have complex multiplication.

Modular form 60690.2.a.by

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

Elliptic curves in class 60690by

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.bx1 60690by1 \([1, 0, 0, -208086, 40058916]\) \(-142843688929/16800000\) \(-117192725008800000\) \([]\) \(783360\) \(2.0111\) \(\Gamma_0(N)\)-optimal