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Properties

Label 9075.h
Number of curves $1$
Conductor $9075$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("h1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 9075.h1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1 - T\)
\(5\)\(1\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 + T + 2 T^{2}\) 1.2.b
\(7\) \( 1 - T + 7 T^{2}\) 1.7.ab
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 3 T + 17 T^{2}\) 1.17.ad
\(19\) \( 1 - 3 T + 19 T^{2}\) 1.19.ad
\(23\) \( 1 - T + 23 T^{2}\) 1.23.ab
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 9075.h do not have complex multiplication.

Modular form 9075.2.a.h

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{6} + q^{7} + 3 q^{8} + q^{9} - q^{12} - 2 q^{13} - q^{14} - q^{16} + 3 q^{17} - q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 9075.h

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9075.h1 9075r1 \([1, 0, 0, -3638, 98517]\) \(-10241915/2187\) \(-1137069140625\) \([]\) \(10080\) \(1.0346\) \(\Gamma_0(N)\)-optimal