Elliptic curve isogeny class with Cremona label 94815c (LMFDB label 94815.bi)

• Label: 94815c
• Number of curves: $2$
• Conductor: $94815$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 94815c have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 94815c do not have complex multiplication.

Modular form 94815.2.a.c

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 94815c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
94815.bi2	94815c1	\([1, -1, 0, -34454310, -77824253809]\)	\(1953326569433829507/262451171875\)	\(607754312017822265625\)	\([2]\)	\(7741440\)	\(3.0069\)	\(\Gamma_0(N)\)-optimal
94815.bi1	94815c2	\([1, -1, 0, -551251185, -4981503081934]\)	\(8000051600110940079507/144453125\)	\(334507973334609375\)	\([2]\)	\(15482880\)	\(3.3535\)