Elliptic curve isogeny class with LMFDB label 30030.a (Cremona label 30030a)

• Label: 30030.a
• Number of curves: $4$
• Conductor: $30030$
• CM: no
• Rank: $1$

Elliptic curves in class 30030.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
30030.a1	30030a4	\([1, 1, 0, -261268, -49896812]\)	\(1972354483749778615369/70549971679687500\)	\(70549971679687500\)	\([2]\)	\(393216\)	\(2.0033\)
30030.a2	30030a2	\([1, 1, 0, -41048, 2119152]\)	\(7649204088039921289/2455152950250000\)	\(2455152950250000\)	\([2, 2]\)	\(196608\)	\(1.6567\)
30030.a3	30030a1	\([1, 1, 0, -37128, 2737728]\)	\(5660393911359932809/1087710624000\)	\(1087710624000\)	\([2]\)	\(98304\)	\(1.3101\)	\(\Gamma_0(N)\)-optimal
30030.a4	30030a3	\([1, 1, 0, 116452, 14624652]\)	\(174646038940465958711/192852576007591500\)	\(-192852576007591500\)	\([2]\)	\(393216\)	\(2.0033\)

Rank

The elliptic curves in class 30030.a have rank \(1\).

Complex multiplication

The elliptic curves in class 30030.a do not have complex multiplication.

Modular form 30030.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.