# Properties

 Label 67280g Number of curves 4 Conductor 67280 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("67280.t1")

sage: E.isogeny_class()

## Elliptic curves in class 67280g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67280.t3 67280g1 [0, 0, 0, -1682, -24389]  50176 $$\Gamma_0(N)$$-optimal
67280.t2 67280g2 [0, 0, 0, -5887, 146334] [2, 2] 100352
67280.t4 67280g3 [0, 0, 0, 10933, 829226]  200704
67280.t1 67280g4 [0, 0, 0, -89987, 10389714]  200704

## Rank

sage: E.rank()

The elliptic curves in class 67280g have rank $$0$$.

## Modular form 67280.2.a.t

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 