# Properties

 Label 3146.a Number of curves 2 Conductor 3146 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3146.a1")

sage: E.isogeny_class()

## Elliptic curves in class 3146.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3146.a1 3146i2 [1, -1, 0, -25735, 1749919] [] 19600
3146.a2 3146i1 [1, -1, 0, -325, -3371] [] 2800 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3146.a have rank $$1$$.

## Modular form3146.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - 3q^{3} + q^{4} - q^{5} + 3q^{6} - q^{7} - q^{8} + 6q^{9} + q^{10} - 3q^{12} + q^{13} + q^{14} + 3q^{15} + q^{16} + 3q^{17} - 6q^{18} - 6q^{19} + O(q^{20})$$

## 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. 