Elliptic curve isogeny class with Cremona label 5415h (LMFDB label 5415.c)

• Label: 5415h
• Number of curves: $2$
• Conductor: $5415$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 5415h have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1 + T$
$5$	$1 + T$
$19$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 - T + 2 T^{2}$	1.2.ab
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 6 T + 11 T^{2}$	1.11.g
$13$	$1 + 13 T^{2}$	1.13.a
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 + 4 T + 29 T^{2}$	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 5415h do not have complex multiplication.

Modular form 5415.2.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.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 5415h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5415.c2	5415h1	$[1, 0, 0, 534, 121371]$	$357911/135375$	$-6368836140375$	$[2]$	$8640$	$1.1360$	$\Gamma_0(N)$-optimal
5415.c1	5415h2	$[1, 0, 0, -33761, 2323110]$	$90458382169/2671875$	$125700713296875$	$[2]$	$17280$	$1.4826$