# Properties

 Label 124215.t Number of curves 4 Conductor 124215 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("124215.t1")

sage: E.isogeny_class()

## Elliptic curves in class 124215.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
124215.t1 124215be4 [1, 1, 1, -931785, 345782562]  1474560
124215.t2 124215be2 [1, 1, 1, -62280, 4588800] [2, 2] 737280
124215.t3 124215be1 [1, 1, 1, -20875, -1108528]  368640 $$\Gamma_0(N)$$-optimal
124215.t4 124215be3 [1, 1, 1, 144745, 28852130]  1474560

## Rank

sage: E.rank()

The elliptic curves in class 124215.t have rank $$1$$.

## Modular form 124215.2.a.t

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 