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Properties

Label 278850.iz
Number of curves $1$
Conductor $278850$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("iz1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 278850.iz1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(11\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 3 T + 7 T^{2}\) 1.7.ad
\(17\) \( 1 + 5 T + 17 T^{2}\) 1.17.f
\(19\) \( 1 - T + 19 T^{2}\) 1.19.ab
\(23\) \( 1 - 3 T + 23 T^{2}\) 1.23.ad
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 278850.iz do not have complex multiplication.

Modular form 278850.2.a.iz

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

Elliptic curves in class 278850.iz

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
278850.iz1 278850iz1 \([1, 0, 0, -88, 18212]\) \(-625/1188\) \(-143356227300\) \([]\) \(338688\) \(0.81969\) \(\Gamma_0(N)\)-optimal