Elliptic curve isogeny class with Cremona label 35378o (LMFDB label 35378.n)

• Label: 35378o
• Number of curves: $3$
• Conductor: $35378$
• CM: no
• Rank: $0$

Elliptic curves in class 35378o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35378.n2	35378o1	$[1, 0, 0, -274548, 55364840]$	$-413493625/152$	$-841304929772888$	$[]$	$272160$	$1.8317$	$\Gamma_0(N)$-optimal
35378.n3	35378o2	$[1, 0, 0, 167677, 210479681]$	$94196375/3511808$	$-19437509097472804352$	$[]$	$816480$	$2.3810$
35378.n1	35378o3	$[1, 0, 0, -1512778, -5760849116]$	$-69173457625/2550136832$	$-14114754528664572919808$	$[]$	$2449440$	$2.9303$

Rank

The elliptic curves in class 35378o have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$7$	$1$
$19$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 - T + 3 T^{2}$	1.3.ab
$5$	$1 + 5 T^{2}$	1.5.a
$11$	$1 - 3 T + 11 T^{2}$	1.11.ad
$13$	$1 - 2 T + 13 T^{2}$	1.13.ac
$17$	$1 - 6 T + 17 T^{2}$	1.17.ag
$23$	$1 + 6 T + 23 T^{2}$	1.23.g
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 35378o do not have complex multiplication.

Modular form 35378.2.a.o

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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.