Elliptic curve isogeny class with Cremona label 98010e (LMFDB label 98010.o)

• Label: 98010e
• Number of curves: $2$
• Conductor: $98010$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 98010e have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 98010e do not have complex multiplication.

Modular form 98010.2.a.e

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 98010e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
98010.o2	98010e1	\([1, -1, 0, 2700, -63024]\)	\(15166431/20480\)	\(-2938807111680\)	\([]\)	\(155520\)	\(1.0782\)	\(\Gamma_0(N)\)-optimal
98010.o1	98010e2	\([1, -1, 0, -26340, 2664800]\)	\(-2146689/2000\)	\(-1882960298802000\)	\([]\)	\(466560\)	\(1.6275\)