Elliptic curve isogeny class with LMFDB label 94815.d (Cremona label 94815w)

• Label: 94815.d
• Number of curves: $4$
• Conductor: $94815$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 94815.d have rank \(2\).

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
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 94815.2.a.d

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 94815.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
94815.d1	94815w4	\([1, -1, 1, -303638, 64475156]\)	\(36097320816649/80625\)	\(6914893505625\)	\([2]\)	\(540672\)	\(1.7089\)
94815.d2	94815w3	\([1, -1, 1, -52268, -3299488]\)	\(184122897769/51282015\)	\(4398259503613815\)	\([2]\)	\(540672\)	\(1.7089\)
94815.d3	94815w2	\([1, -1, 1, -19193, 987032]\)	\(9116230969/416025\)	\(35680850489025\)	\([2, 2]\)	\(270336\)	\(1.3623\)
94815.d4	94815w1	\([1, -1, 1, 652, 58286]\)	\(357911/17415\)	\(-1493616997215\)	\([2]\)	\(135168\)	\(1.0158\)	\(\Gamma_0(N)\)-optimal