# Properties

 Label 212160.cc Number of curves 8 Conductor 212160 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("212160.cc1")

sage: E.isogeny_class()

## Elliptic curves in class 212160.cc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
212160.cc1 212160gf8 [0, -1, 0, -421824000385, -105449485114502783] [2] 637009920
212160.cc2 212160gf6 [0, -1, 0, -26364000385, -1647641566502783] [2, 2] 318504960
212160.cc3 212160gf7 [0, -1, 0, -26316193665, -1653914697371775] [2] 637009920
212160.cc4 212160gf5 [0, -1, 0, -5207889025, -144637146850175] [2] 212336640
212160.cc5 212160gf3 [0, -1, 0, -1650738305, -25645921710975] [2] 159252480
212160.cc6 212160gf2 [0, -1, 0, -355665025, -1815815189375] [2, 2] 106168320
212160.cc7 212160gf1 [0, -1, 0, -134153345, 575935024257] [2] 53084160 $$\Gamma_0(N)$$-optimal
212160.cc8 212160gf4 [0, -1, 0, 952372095, -12070041387903] [2] 212336640

## Rank

sage: E.rank()

The elliptic curves in class 212160.cc have rank $$1$$.

## Modular form 212160.2.a.cc

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 4q^{7} + q^{9} - q^{13} - q^{15} + q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.