Properties

 Label 172480dk Number of curves 4 Conductor 172480 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("172480.gt1")

sage: E.isogeny_class()

Elliptic curves in class 172480dk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
172480.gt4 172480dk1 [0, -1, 0, -8885, 318725] [2] 331776 $$\Gamma_0(N)$$-optimal
172480.gt3 172480dk2 [0, -1, 0, -19665, -593263] [2] 663552
172480.gt2 172480dk3 [0, -1, 0, -87285, -9771355] [2] 995328
172480.gt1 172480dk4 [0, -1, 0, -1391665, -631438863] [2] 1990656

Rank

sage: E.rank()

The elliptic curves in class 172480dk have rank $$0$$.

Modular form 172480.2.a.gt

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} + q^{9} - q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.