Elliptic curve isogeny class with Cremona label 70602u (LMFDB label 70602.w)

• Label: 70602u
• Number of curves: $4$
• Conductor: $70602$
• CM: no
• Rank: $1$

Elliptic curves in class 70602u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
70602.w4	70602u1	\([1, 1, 1, -171497, 32769479]\)	\(-117433042273/30128112\)	\(-143111672584522992\)	\([2]\)	\(860160\)	\(2.0092\)	\(\Gamma_0(N)\)-optimal
70602.w3	70602u2	\([1, 1, 1, -2894717, 1894362671]\)	\(564727473247393/26687556\)	\(126768672937524996\)	\([2, 2]\)	\(1720320\)	\(2.3558\)
70602.w2	70602u3	\([1, 1, 1, -3046007, 1685158859]\)	\(657980877056833/122123738898\)	\(580100490066166466418\)	\([2]\)	\(3440640\)	\(2.7023\)
70602.w1	70602u4	\([1, 1, 1, -46314947, 121299995171]\)	\(2313045024604457473/5166\)	\(24539038509006\)	\([2]\)	\(3440640\)	\(2.7023\)

Rank

The elliptic curves in class 70602u have rank \(1\).

Complex multiplication

The elliptic curves in class 70602u do not have complex multiplication.

Modular form 70602.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.