Elliptic curve isogeny class with Cremona label 32634u (LMFDB label 32634.bc)

• Label: 32634u
• Number of curves: $2$
• Conductor: $32634$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 32634u have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(37\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32634u do not have complex multiplication.

Modular form 32634.2.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.

Elliptic curves in class 32634u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32634.bc2	32634u1	\([1, -1, 0, -64836, -6677168]\)	\(-351447414193/22278144\)	\(-1910709993959424\)	\([2]\)	\(184320\)	\(1.6858\)	\(\Gamma_0(N)\)-optimal
32634.bc1	32634u2	\([1, -1, 0, -1052676, -415445360]\)	\(1504154129818033/5519808\)	\(473412520824768\)	\([2]\)	\(368640\)	\(2.0323\)