# Properties

 Label 294.g Number of curves $6$ Conductor $294$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("294.g1")

sage: E.isogeny_class()

## Elliptic curves in class 294.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
294.g1 294c3 [1, 0, 0, -65857, -6510547] [2] 768
294.g2 294c5 [1, 0, 0, -44787, 3609423] [2] 1536
294.g3 294c4 [1, 0, 0, -5097, -49995] [2, 2] 768
294.g4 294c2 [1, 0, 0, -4117, -101935] [2, 2] 384
294.g5 294c1 [1, 0, 0, -197, -2367] [4] 192 $$\Gamma_0(N)$$-optimal
294.g6 294c6 [1, 0, 0, 18913, -381333] [2] 1536

## Rank

sage: E.rank()

The elliptic curves in class 294.g have rank $$0$$.

## Modular form294.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} - 6q^{13} + 2q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.