Elliptic curve isogeny class with LMFDB label 130.a (Cremona label 130a)

• Label: 130.a
• Number of curves: $4$
• Conductor: $130$
• CM: no
• Rank: $1$

Elliptic curves in class 130.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
130.a1	130a3	\([1, 0, 1, -208, -1122]\)	\(988345570681/44994560\)	\(44994560\)	\([2]\)	\(72\)	\(0.23045\)
130.a2	130a1	\([1, 0, 1, -33, 68]\)	\(3803721481/26000\)	\(26000\)	\([6]\)	\(24\)	\(-0.31886\)	\(\Gamma_0(N)\)-optimal
130.a3	130a2	\([1, 0, 1, -13, 156]\)	\(-217081801/10562500\)	\(-10562500\)	\([6]\)	\(48\)	\(0.027717\)
130.a4	130a4	\([1, 0, 1, 112, -4194]\)	\(157376536199/7722894400\)	\(-7722894400\)	\([2]\)	\(144\)	\(0.57702\)

Rank

The elliptic curves in class 130.a have rank \(1\).

Complex multiplication

The elliptic curves in class 130.a do not have complex multiplication.

Modular form 130.2.a.a

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.