Elliptic curve isogeny class with Cremona label 11270u (LMFDB label 11270.r)

• Label: 11270u
• Number of curves: $4$
• Conductor: $11270$
• CM: no
• Rank: $1$

Elliptic curves in class 11270u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11270.r4	11270u1	\([1, 1, 1, -90210, -10421713]\)	\(690080604747409/3406760000\)	\(400801907240000\)	\([2]\)	\(119808\)	\(1.6497\)	\(\Gamma_0(N)\)-optimal
11270.r3	11270u2	\([1, 1, 1, -139210, 2083087]\)	\(2535986675931409/1450751712200\)	\(170679488188617800\)	\([2]\)	\(239616\)	\(1.9963\)
11270.r2	11270u3	\([1, 1, 1, -518470, 135980095]\)	\(131010595463836369/7704101562500\)	\(906379844726562500\)	\([2]\)	\(359424\)	\(2.1990\)
11270.r1	11270u4	\([1, 1, 1, -8174720, 8992730095]\)	\(513516182162686336369/1944885031250\)	\(228813779041531250\)	\([2]\)	\(718848\)	\(2.5456\)

Rank

The elliptic curves in class 11270u have rank \(1\).

Complex multiplication

The elliptic curves in class 11270u do not have complex multiplication.

Modular form 11270.2.a.u

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.