Elliptic curve isogeny class with Cremona label 57434h (LMFDB label 57434.e)

• Label: 57434h
• Number of curves: $2$
• Conductor: $57434$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 57434h have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(13\)	\(1 - T\)
\(47\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 57434h do not have complex multiplication.

Modular form 57434.2.a.h

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 57434h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57434.e2	57434h1	\([1, -1, 1, -5937, -267807]\)	\(-2146689/1664\)	\(-17936614307456\)	\([]\)	\(196420\)	\(1.2419\)	\(\Gamma_0(N)\)-optimal
57434.e1	57434h2	\([1, -1, 1, -469827, 136115853]\)	\(-1064019559329/125497034\)	\(-1352759552636834186\)	\([]\)	\(1374940\)	\(2.2149\)