Elliptic curve isogeny class with LMFDB label 361.a (Cremona label 361a)

• Label: 361.a
• Number of curves: $2$
• Conductor: $361$
• CM: \(\Q(\sqrt{-19}) \)
• Rank: $1$

Rank

The elliptic curves in class 361.a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 361.a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-19}) \).

Modular form 361.2.a.a

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 361.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
361.a1	361a2	\([0, 0, 1, -13718, -619025]\)	\(-884736\)	\(-322687697779\)	\([]\)	\(380\)	\(1.1221\)		\(-19\)
361.a2	361a1	\([0, 0, 1, -38, 90]\)	\(-884736\)	\(-6859\)	\([]\)	\(20\)	\(-0.35015\)	\(\Gamma_0(N)\)-optimal	\(-19\)