Properties

 Label 187200mp Number of curves $6$ Conductor $187200$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("187200.jc1")

sage: E.isogeny_class()

Elliptic curves in class 187200mp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
187200.jc6 187200mp1 [0, 0, 0, 215700, -15442000] [2] 2359296 $$\Gamma_0(N)$$-optimal
187200.jc5 187200mp2 [0, 0, 0, -936300, -128338000] [2, 2] 4718592
187200.jc3 187200mp3 [0, 0, 0, -8136300, 8842862000] [2, 2] 9437184
187200.jc2 187200mp4 [0, 0, 0, -12168300, -16324882000] [2] 9437184
187200.jc1 187200mp5 [0, 0, 0, -129816300, 569300942000] [2] 18874368
187200.jc4 187200mp6 [0, 0, 0, -1656300, 22541582000] [2] 18874368

Rank

sage: E.rank()

The elliptic curves in class 187200mp have rank $$1$$.

Modular form 187200.2.a.jc

sage: E.q_eigenform(10)

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

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.