Elliptic curve isogeny class with Cremona label 121275dj (LMFDB label 121275.bb)

• Label: 121275dj
• Number of curves: $4$
• Conductor: $121275$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 121275dj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 121275dj do not have complex multiplication.

Modular form 121275.2.a.dj

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.

Elliptic curves in class 121275dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121275.bb4	121275dj1	\([1, -1, 1, -404480, 133336522]\)	\(-5461074081/2562175\)	\(-3433559548018359375\)	\([2]\)	\(2359296\)	\(2.2627\)	\(\Gamma_0(N)\)-optimal
121275.bb3	121275dj2	\([1, -1, 1, -7074605, 7243689772]\)	\(29220958012401/3705625\)	\(4965891908291015625\)	\([2, 2]\)	\(4718592\)	\(2.6093\)
121275.bb2	121275dj3	\([1, -1, 1, -7680980, 5929068772]\)	\(37397086385121/10316796875\)	\(13825494517401123046875\)	\([2]\)	\(9437184\)	\(2.9559\)
121275.bb1	121275dj4	\([1, -1, 1, -113190230, 463540877272]\)	\(119678115308998401/1925\)	\(2579684108203125\)	\([2]\)	\(9437184\)	\(2.9559\)