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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("p1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 9075.p1 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.ab
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 + 3 T + 17 T^{2}\) 1.17.d
\(19\) \( 1 + 3 T + 19 T^{2}\) 1.19.d
\(23\) \( 1 - T + 23 T^{2}\) 1.23.ab
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 9075.2.a.p

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.p

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9075.p1 9075p1 \([1, 0, 1, -440201, -131566327]\) \(-10241915/2187\) \(-2014387343834765625\) \([]\) \(110880\) \(2.2335\) \(\Gamma_0(N)\)-optimal