# Properties

 Label 2790g Number of curves $6$ Conductor $2790$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2790.c1")

sage: E.isogeny_class()

## Elliptic curves in class 2790g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2790.c6 2790g1 [1, -1, 0, 540, 27216]  4096 $$\Gamma_0(N)$$-optimal
2790.c5 2790g2 [1, -1, 0, -10980, 421200] [2, 2] 8192
2790.c4 2790g3 [1, -1, 0, -33300, -1815264]  16384
2790.c2 2790g4 [1, -1, 0, -172980, 27734400] [2, 2] 16384
2790.c1 2790g5 [1, -1, 0, -2767680, 1772929620]  32768
2790.c3 2790g6 [1, -1, 0, -170280, 28639980]  32768

## Rank

sage: E.rank()

The elliptic curves in class 2790g have rank $$0$$.

## Modular form2790.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + 4q^{11} + 6q^{13} + q^{16} - 2q^{17} + 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 