Elliptic curve isogeny class with Cremona label 33075ca (LMFDB label 33075.h)

• Label: 33075ca
• Number of curves: $1$
• Conductor: $33075$
• CM: no
• Rank: $1$

Rank

The elliptic curve 33075ca1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 33075ca do not have complex multiplication.

Modular form 33075.2.a.ca

Isogeny graph

Elliptic curves in class 33075ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33075.h1	33075ca1	\([1, -1, 1, -230, -318]\)	\(1875\)	\(714717675\)	\([]\)	\(13824\)	\(0.39028\)	\(\Gamma_0(N)\)-optimal