Elliptic curve isogeny class with Cremona label 105a (LMFDB label 105.a)

• Label: 105a
• Number of curves: $4$
• Conductor: $105$
• CM: no
• Rank: $0$

Elliptic curves in class 105a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
105.a3	105a1	\([1, 0, 1, -3, 1]\)	\(1771561/105\)	\(105\)	\([2]\)	\(4\)	\(-0.85911\)	\(\Gamma_0(N)\)-optimal
105.a2	105a2	\([1, 0, 1, -8, -7]\)	\(47045881/11025\)	\(11025\)	\([2, 2]\)	\(8\)	\(-0.51254\)
105.a1	105a3	\([1, 0, 1, -113, -469]\)	\(157551496201/13125\)	\(13125\)	\([2]\)	\(16\)	\(-0.16596\)
105.a4	105a4	\([1, 0, 1, 17, -37]\)	\(590589719/972405\)	\(-972405\)	\([4]\)	\(16\)	\(-0.16596\)

Rank

The elliptic curves in class 105a have rank \(0\).

Complex multiplication

The elliptic curves in class 105a do not have complex multiplication.

Modular form 105.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.