# Properties

 Label 22080cr Number of curves $6$ Conductor $22080$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("22080.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 22080cr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22080.bv5 22080cr1 [0, 1, 0, -26881, -1870081] [2] 73728 $$\Gamma_0(N)$$-optimal
22080.bv4 22080cr2 [0, 1, 0, -441601, -113097985] [2, 2] 147456
22080.bv3 22080cr3 [0, 1, 0, -453121, -106897921] [2, 2] 294912
22080.bv1 22080cr4 [0, 1, 0, -7065601, -7231248385] [2] 294912
22080.bv6 22080cr5 [0, 1, 0, 562559, -517029505] [2] 589824
22080.bv2 22080cr6 [0, 1, 0, -1653121, 700222079] [2] 589824

## Rank

sage: E.rank()

The elliptic curves in class 22080cr have rank $$0$$.

## Modular form 22080.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + 4q^{11} + 2q^{13} - q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.