Elliptic curve isogeny class with Cremona label 372645dr (LMFDB label 372645.dr)

• Label: 372645dr
• Number of curves: $2$
• Conductor: $372645$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 372645dr have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 372645dr do not have complex multiplication.

Modular form 372645.2.a.dr

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 372645dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
372645.dr2	372645dr1	\([1, -1, 0, -44550, 4534375]\)	\(-51895117/16875\)	\(-3179725332249375\)	\([2]\)	\(1658880\)	\(1.6872\)	\(\Gamma_0(N)\)-optimal
372645.dr1	372645dr2	\([1, -1, 0, -761175, 255783100]\)	\(258840217117/18225\)	\(3434103358829325\)	\([2]\)	\(3317760\)	\(2.0338\)