Elliptic curve isogeny class with Cremona label 13650di (LMFDB label 13650.di)

• Label: 13650di
• Number of curves: $2$
• Conductor: $13650$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 13650di have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13650di do not have complex multiplication.

Modular form 13650.2.a.di

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.

Elliptic curves in class 13650di

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13650.di2	13650di1	\([1, 0, 0, -8638, -2204608]\)	\(-36495256013/1053197964\)	\(-2057027273437500\)	\([2]\)	\(105600\)	\(1.6188\)	\(\Gamma_0(N)\)-optimal
13650.di1	13650di2	\([1, 0, 0, -312388, -66903358]\)	\(1726143065560493/9662982966\)	\(18873013605468750\)	\([2]\)	\(211200\)	\(1.9654\)