Properties

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

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14994.i1")

sage: E.isogeny_class()

Elliptic curves in class 14994bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14994.i5 14994bh1 [1, -1, 0, -15003, 659749] [2] 49152 $$\Gamma_0(N)$$-optimal
14994.i4 14994bh2 [1, -1, 0, -50283, -3566795] [2, 2] 98304
14994.i2 14994bh3 [1, -1, 0, -764703, -257185895] [2, 2] 196608
14994.i6 14994bh4 [1, -1, 0, 99657, -20869871] [2] 196608
14994.i1 14994bh5 [1, -1, 0, -12235113, -16469463389] [2] 393216
14994.i3 14994bh6 [1, -1, 0, -725013, -285103841] [2] 393216

Rank

sage: E.rank()

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

Modular form 14994.2.a.i

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.