Elliptic curve isogeny class with Cremona label 42432e (LMFDB label 42432.bc)

• Label: 42432e
• Number of curves: $2$
• Conductor: $42432$
• CM: no
• Rank: $0$

Elliptic curves in class 42432e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42432.bc1	42432e1	$[0, -1, 0, -4997, 137637]$	$13478411517952/304317$	$311620608$	$[2]$	$30720$	$0.74390$	$\Gamma_0(N)$-optimal
42432.bc2	42432e2	$[0, -1, 0, -4817, 147825]$	$-754612278352/127035441$	$-2081348665344$	$[2]$	$61440$	$1.0905$

Rank

The elliptic curves in class 42432e have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$13$	$1 + T$
$17$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$7$	$1 - 4 T + 7 T^{2}$	1.7.ae
$11$	$1 + 11 T^{2}$	1.11.a
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 42432e do not have complex multiplication.

Modular form 42432.2.a.e

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.