# Properties

 Label 380880ex Number of curves $6$ Conductor $380880$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("380880.ex1")

sage: E.isogeny_class()

## Elliptic curves in class 380880ex

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
380880.ex5 380880ex1 [0, 0, 0, -31995507, -76424358094]  38928384 $$\Gamma_0(N)$$-optimal
380880.ex4 380880ex2 [0, 0, 0, -525615987, -4638168661966] [2, 2] 77856768
380880.ex3 380880ex3 [0, 0, 0, -539327667, -4383413874574] [2, 2] 155713536
380880.ex1 380880ex4 [0, 0, 0, -8409831987, -296844558897166]  155713536
380880.ex2 380880ex5 [0, 0, 0, -1967627667, 28776284585426]  311427072
380880.ex6 380880ex6 [0, 0, 0, 669585453, -21238805941486]  311427072

## Rank

sage: E.rank()

The elliptic curves in class 380880ex have rank $$1$$.

## Modular form 380880.2.a.ex

sage: E.q_eigenform(10)

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

## 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. 