Elliptic curve isogeny class with Cremona label 17784i (LMFDB label 17784.b)

• Label: 17784i
• Number of curves: $2$
• Conductor: $17784$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 17784i have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1 + T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17784i do not have complex multiplication.

Modular form 17784.2.a.i

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 17784i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17784.b1	17784i1	\([0, 0, 0, -246, 1485]\)	\(3811055616/247\)	\(106704\)	\([2]\)	\(3328\)	\(0.021945\)	\(\Gamma_0(N)\)-optimal
17784.b2	17784i2	\([0, 0, 0, -231, 1674]\)	\(-197222256/61009\)	\(-421694208\)	\([2]\)	\(6656\)	\(0.36852\)