# Properties

 Label 14994bi Number of curves $6$ Conductor $14994$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14994.g1")

sage: E.isogeny_class()

## Elliptic curves in class 14994bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14994.g5 14994bi1 [1, -1, 0, -30977613, 66286809189] [2] 1474560 $$\Gamma_0(N)$$-optimal
14994.g4 14994bi2 [1, -1, 0, -40009293, 24490000485] [2, 2] 2949120
14994.g2 14994bi3 [1, -1, 0, -378838413, -2818625145435] [2, 2] 5898240
14994.g6 14994bi4 [1, -1, 0, 154312947, 192501009189] [2] 5898240
14994.g1 14994bi5 [1, -1, 0, -6049904373, -181120341567411] [2] 11796480
14994.g3 14994bi6 [1, -1, 0, -129038373, -6480344011779] [2] 11796480

## Rank

sage: E.rank()

The elliptic curves in class 14994bi have rank $$0$$.

## Modular form 14994.2.a.g

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.