# Properties

 Label 48400.m Number of curves 2 Conductor 48400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("48400.m1")

sage: E.isogeny_class()

## Elliptic curves in class 48400.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
48400.m1 48400co2 [0, 1, 0, -20808, -1193612] [] 124416
48400.m2 48400co1 [0, 1, 0, 1192, -5612] [] 41472 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 48400.m have rank $$1$$.

## Modular form 48400.2.a.m

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{7} + q^{9} + 5q^{13} + 3q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 