# Properties

 Label 67240.g Number of curves 4 Conductor 67240 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("67240.g1")

sage: E.isogeny_class()

## Elliptic curves in class 67240.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67240.g1 67240e4 [0, 0, 0, -179867, -29360346]  276480
67240.g2 67240e2 [0, 0, 0, -11767, -413526] [2, 2] 138240
67240.g3 67240e1 [0, 0, 0, -3362, 68921]  69120 $$\Gamma_0(N)$$-optimal
67240.g4 67240e3 [0, 0, 0, 21853, -2343314]  276480

## Rank

sage: E.rank()

The elliptic curves in class 67240.g have rank $$0$$.

## Modular form 67240.2.a.g

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 LMFDB 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 LMFDB labels. 