Properties

Label 180918bv
Number of curves $1$
Conductor $180918$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 180918bv1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(19\)\(1 + T\)
\(23\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(11\) \( 1 + T + 11 T^{2}\) 1.11.b
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(29\) \( 1 - 9 T + 29 T^{2}\) 1.29.aj
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 180918bv do not have complex multiplication.

Modular form 180918.2.a.bv

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

Elliptic curves in class 180918bv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180918.t1 180918bv1 \([1, -1, 0, -11126556, 35538564784]\) \(-1411599396089233/4238100157152\) \(-457367983913141264505312\) \([]\) \(27878400\) \(3.2268\) \(\Gamma_0(N)\)-optimal