# Properties

 Label 294.f Number of curves 2 Conductor 294 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("294.f1")

sage: E.isogeny_class()

## Elliptic curves in class 294.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
294.f1 294b2 [1, 0, 0, -141, 657]  84
294.f2 294b1 [1, 0, 0, -1, -1] [] 12 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 294.f have rank $$0$$.

## Modular form294.2.a.f

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + 5q^{11} + q^{12} - q^{15} + q^{16} + 4q^{17} + q^{18} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 