# Properties

 Label 12480.o Number of curves $6$ Conductor $12480$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("12480.o1")

sage: E.isogeny_class()

## Elliptic curves in class 12480.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12480.o1 12480bl5 [0, -1, 0, -576961, 168874081] [2] 98304
12480.o2 12480bl3 [0, -1, 0, -54081, -4818975] [2] 49152
12480.o3 12480bl4 [0, -1, 0, -36161, 2632161] [2, 2] 49152
12480.o4 12480bl6 [0, -1, 0, -7361, 6681441] [2] 98304
12480.o5 12480bl2 [0, -1, 0, -4161, -36639] [2, 2] 24576
12480.o6 12480bl1 [0, -1, 0, 959, -4895] [2] 12288 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 12480.o have rank $$0$$.

## Modular form 12480.2.a.o

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.