Elliptic curve isogeny class with Cremona label 270504bv (LMFDB label 270504.bv)

• Label: 270504bv
• Number of curves: $4$
• Conductor: $270504$
• CM: no
• Rank: $1$

Elliptic curves in class 270504bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
270504.bv3	270504bv1	$[0, 0, 0, -19074, -584647]$	$2725888/1053$	$296462256871248$	$[2]$	$655360$	$1.4759$	$\Gamma_0(N)$-optimal
270504.bv2	270504bv2	$[0, 0, 0, -136119, 18915050]$	$61918288/1521$	$6851572158802176$	$[2, 2]$	$1310720$	$1.8225$
270504.bv1	270504bv3	$[0, 0, 0, -2164899, 1226039150]$	$62275269892/39$	$702725349620736$	$[2]$	$2621440$	$2.1690$
270504.bv4	270504bv4	$[0, 0, 0, 19941, 59771558]$	$48668/85683$	$-1543887593116756992$	$[2]$	$2621440$	$2.1690$

Rank

The elliptic curves in class 270504bv 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 $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 11 T^{2}$	1.11.a
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 270504bv do not have complex multiplication.

Modular form 270504.2.a.bv

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.

$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.