Elliptic curve isogeny class with Cremona label 225318c (LMFDB label 225318.be)

• Label: 225318c
• Number of curves: $2$
• Conductor: $225318$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 225318c have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(17\)	\(1 + T\)
\(47\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 225318c do not have complex multiplication.

Modular form 225318.2.a.c

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 225318c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
225318.be2	225318c1	\([1, 0, 0, -2401229, 1436338065]\)	\(-142048716869233/500723712\)	\(-5397408711984181248\)	\([2]\)	\(6782976\)	\(2.4568\)	\(\Gamma_0(N)\)-optimal
225318.be1	225318c2	\([1, 0, 0, -38452109, 91772633169]\)	\(583306826994199153/7210176\)	\(77720039663987904\)	\([2]\)	\(13565952\)	\(2.8033\)