Elliptic curve isogeny class with Cremona label 7650u (LMFDB label 7650.bc)

• Label: 7650u
• Number of curves: $2$
• Conductor: $7650$
• CM: no
• Rank: $1$

Elliptic curves in class 7650u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7650.bc1	7650u1	$[1, -1, 0, -1692, -22784]$	$47045881/6800$	$77456250000$	$[2]$	$9216$	$0.81473$	$\Gamma_0(N)$-optimal
7650.bc2	7650u2	$[1, -1, 0, 2808, -126284]$	$214921799/722500$	$-8229726562500$	$[2]$	$18432$	$1.1613$

Rank

The elliptic curves in class 7650u have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1$
$5$	$1$
$17$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 - T + 7 T^{2}$	1.7.ab
$11$	$1 + 3 T + 11 T^{2}$	1.11.d
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$19$	$1 - 5 T + 19 T^{2}$	1.19.af
$23$	$1 + 23 T^{2}$	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 7650u do not have complex multiplication.

Modular form 7650.2.a.u

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.