Elliptic curve isogeny class with Cremona label 75504bv (LMFDB label 75504.bh)

• Label: 75504bv
• Number of curves: $2$
• Conductor: $75504$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 75504bv have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 75504bv do not have complex multiplication.

Modular form 75504.2.a.bv

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 75504bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
75504.bh2	75504bv1	\([0, -1, 0, -642792, -508532880]\)	\(-4047806261953/13066420224\)	\(-94814046119729823744\)	\([2]\)	\(2903040\)	\(2.5196\)	\(\Gamma_0(N)\)-optimal
75504.bh1	75504bv2	\([0, -1, 0, -14272232, -20723718288]\)	\(44308125149913793/61165323648\)	\(443834785493706866688\)	\([2]\)	\(5806080\)	\(2.8662\)