Elliptic curve isogeny class with LMFDB label 1694.f (Cremona label 1694h)

• Label: 1694.f
• Number of curves: $1$
• Conductor: $1694$
• CM: no
• Rank: $0$

Rank

The elliptic curve 1694.f1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(7\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1694.f do not have complex multiplication.

Modular form 1694.2.a.f

Isogeny graph

Elliptic curves in class 1694.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1694.f1	1694h1	\([1, 1, 1, 3, 1]\)	\(24167/14\)	\(-1694\)	\([]\)	\(96\)	\(-0.69097\)	\(\Gamma_0(N)\)-optimal