Elliptic curve isogeny class with Cremona label 212415bh (LMFDB label 212415.bo)

• Label: 212415bh
• Number of curves: $2$
• Conductor: $212415$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 212415bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 212415bh do not have complex multiplication.

Modular form 212415.2.a.bh

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 212415bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
212415.bo2	212415bh1	\([0, 1, 1, -62752111, -11704670834]\)	\(115220905984/66430125\)	\(15755874886006697198980125\)	\([]\)	\(42301440\)	\(3.5245\)	\(\Gamma_0(N)\)-optimal
212415.bo1	212415bh2	\([0, 1, 1, -3377700601, 75556192602055]\)	\(17968412610002944/158203125\)	\(37522564409976321251953125\)	\([]\)	\(126904320\)	\(4.0738\)