Elliptic curve isogeny class with LMFDB label 35904.bh (Cremona label 35904bx)

• Label: 35904.bh
• Number of curves: $4$
• Conductor: $35904$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 35904.bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 35904.bh do not have complex multiplication.

Modular form 35904.2.a.bh

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 35904.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35904.bh1	35904bx4	\([0, -1, 0, -101523617, -393696369087]\)	\(441453577446719855661097/4354701912\)	\(1141558978019328\)	\([2]\)	\(2064384\)	\(2.9211\)
35904.bh2	35904bx2	\([0, -1, 0, -6345377, -6149611455]\)	\(107784459654566688937/10704361149504\)	\(2806084049175576576\)	\([2, 2]\)	\(1032192\)	\(2.5745\)
35904.bh3	35904bx3	\([0, -1, 0, -5866657, -7117104575]\)	\(-85183593440646799657/34223681512621656\)	\(-8971532766444691390464\)	\([2]\)	\(2064384\)	\(2.9211\)
35904.bh4	35904bx1	\([0, -1, 0, -426657, -80555967]\)	\(32765849647039657/8229948198912\)	\(2157431540655587328\)	\([2]\)	\(516096\)	\(2.2279\)	\(\Gamma_0(N)\)-optimal