Properties

 Label 31680.eh Number of curves 4 Conductor 31680 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("31680.eh1")

sage: E.isogeny_class()

Elliptic curves in class 31680.eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
31680.eh1 31680ee4 [0, 0, 0, -255612, -49741616] [2] 165888
31680.eh2 31680ee3 [0, 0, 0, -16032, -771464] [2] 82944
31680.eh3 31680ee2 [0, 0, 0, -3612, -47216] [2] 55296
31680.eh4 31680ee1 [0, 0, 0, -1632, 24856] [2] 27648 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 31680.eh have rank $$1$$.

Modular form 31680.2.a.eh

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} + q^{11} + 4q^{13} - 4q^{19} + O(q^{20})$$

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 LMFDB 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 LMFDB labels.