Elliptic curve isogeny class with LMFDB label 1305.e (Cremona label 1305c)

• Label: 1305.e
• Number of curves: $4$
• Conductor: $1305$
• CM: no
• Rank: $0$

Elliptic curves in class 1305.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1305.e1	1305c3	\([1, -1, 0, -62640, 6049971]\)	\(37286818682653441/1305\)	\(951345\)	\([2]\)	\(2560\)	\(1.0934\)
1305.e2	1305c2	\([1, -1, 0, -3915, 95256]\)	\(9104453457841/1703025\)	\(1241505225\)	\([2, 2]\)	\(1280\)	\(0.74685\)
1305.e3	1305c4	\([1, -1, 0, -3510, 115425]\)	\(-6561258219361/3978455625\)	\(-2900294150625\)	\([2]\)	\(2560\)	\(1.0934\)
1305.e4	1305c1	\([1, -1, 0, -270, 1215]\)	\(2992209121/951345\)	\(693530505\)	\([2]\)	\(640\)	\(0.40028\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 1305.e have rank \(0\).

Complex multiplication

The elliptic curves in class 1305.e do not have complex multiplication.

Modular form 1305.2.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 LMFDB 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 LMFDB labels.