Properties

 Label 148800et Number of curves $6$ Conductor $148800$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("148800.ci1")

sage: E.isogeny_class()

Elliptic curves in class 148800et

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
148800.ci6 148800et1 [0, -1, 0, 95967, 64799937] [2] 2359296 $$\Gamma_0(N)$$-optimal
148800.ci5 148800et2 [0, -1, 0, -1952033, 992543937] [2, 2] 4718592
148800.ci2 148800et3 [0, -1, 0, -30752033, 65648543937] [2, 2] 9437184
148800.ci4 148800et4 [0, -1, 0, -5920033, -4320608063] [2] 9437184
148800.ci1 148800et5 [0, -1, 0, -492032033, 4201023743937] [2] 18874368
148800.ci3 148800et6 [0, -1, 0, -30272033, 67796543937] [2] 18874368

Rank

sage: E.rank()

The elliptic curves in class 148800et have rank $$1$$.

Modular form 148800.2.a.ci

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} + 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.