Elliptic curve isogeny class with Cremona label 135252e (LMFDB label 135252.g)

• Label: 135252e
• Number of curves: $2$
• Conductor: $135252$
• CM: no
• Rank: $1$

Elliptic curves in class 135252e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
135252.g1	135252e1	$[0, 0, 0, -3249516, -2254590439]$	$13478411517952/304317$	$85677592235790672$	$[2]$	$2211840$	$2.3632$	$\Gamma_0(N)$-optimal
135252.g2	135252e2	$[0, 0, 0, -3132471, -2424516370]$	$-754612278352/127035441$	$-572250158275316541696$	$[2]$	$4423680$	$2.7098$

Rank

The elliptic curves in class 135252e have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 3 T + 5 T^{2}$	1.5.d
$7$	$1 + T + 7 T^{2}$	1.7.b
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$19$	$1 - 7 T + 19 T^{2}$	1.19.ah
$23$	$1 + 9 T + 23 T^{2}$	1.23.j
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 135252e do not have complex multiplication.

Modular form 135252.2.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.