# Properties

 Label 31680.cc Number of curves $4$ Conductor $31680$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cc1")

sage: E.isogeny_class()

## Elliptic curves in class 31680.cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
31680.cc1 31680bo4 [0, 0, 0, -255612, 49741616]  165888
31680.cc2 31680bo3 [0, 0, 0, -16032, 771464]  82944
31680.cc3 31680bo2 [0, 0, 0, -3612, 47216]  55296
31680.cc4 31680bo1 [0, 0, 0, -1632, -24856]  27648 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 31680.cc do not have complex multiplication.

## Modular form 31680.2.a.cc

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. 