Elliptic curve isogeny class with Cremona label 364815be (LMFDB label 364815.be)

• Label: 364815be
• Number of curves: $2$
• Conductor: $364815$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 364815be have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(67\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 364815be do not have complex multiplication.

Modular form 364815.2.a.be

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 364815be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
364815.be2	364815be1	\([1, -1, 0, -60099, 5376168]\)	\(501891267123/30861875\)	\(1476189741695625\)	\([2]\)	\(1658880\)	\(1.6625\)	\(\Gamma_0(N)\)-optimal
364815.be1	364815be2	\([1, -1, 0, -181704, -23152365]\)	\(13870708507683/3166796875\)	\(151474693644140625\)	\([2]\)	\(3317760\)	\(2.0091\)