# Properties

 Label 67760.ba Number of curves $4$ Conductor $67760$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("67760.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 67760.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67760.ba1 67760ba4 [0, 0, 0, -518243, -143590942]  491520
67760.ba2 67760ba3 [0, 0, 0, -169763, 25158562]  491520
67760.ba3 67760ba2 [0, 0, 0, -34243, -1972542] [2, 2] 245760
67760.ba4 67760ba1 [0, 0, 0, 4477, -183678]  122880 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 67760.ba have rank $$1$$.

## Modular form 67760.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 3q^{9} + 6q^{13} - 2q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 