Elliptic curve isogeny class with Cremona label 414736bc (LMFDB label 414736.bc)

• Label: 414736bc
• Number of curves: $4$
• Conductor: $414736$
• CM: \(\Q(\sqrt{-7}) \)
• Rank: $0$

Elliptic curves in class 414736bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
414736.bc4	414736bc1	\([0, 0, 0, -18515, -1192366]\)	\(-3375\)	\(-207979765460992\)	\([2]\)	\(720896\)	\(1.4618\)	\(\Gamma_0(N)\)-optimal^*	\(-7\)
414736.bc3	414736bc2	\([0, 0, 0, -314755, -67964862]\)	\(16581375\)	\(207979765460992\)	\([2]\)	\(1441792\)	\(1.8083\)	\(\Gamma_0(N)\)-optimal^*	\(-28\)
414736.bc2	414736bc3	\([0, 0, 0, -907235, 408981538]\)	\(-3375\)	\(-24468611426720247808\)	\([2]\)	\(5046272\)	\(2.4347\)	\(\Gamma_0(N)\)-optimal^*	\(-7\)
414736.bc1	414736bc4	\([0, 0, 0, -15422995, 23311947666]\)	\(16581375\)	\(24468611426720247808\)	\([2]\)	\(10092544\)	\(2.7813\)	\(\Gamma_0(N)\)-optimal^*	\(-28\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 414736bc1.

Rank

The elliptic curves in class 414736bc have rank \(0\).

Complex multiplication

Each elliptic curve in class 414736bc has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-7}) \).

Modular form 414736.2.a.bc

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.