# Properties

 Label 348480.qt Number of curves 4 Conductor 348480 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("348480.qt1")

sage: E.isogeny_class()

## Elliptic curves in class 348480.qt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348480.qt1 348480qt4 [0, 0, 0, -30929052, -66206090896]  19906560
348480.qt2 348480qt3 [0, 0, 0, -1939872, -1026818584]  9953280
348480.qt3 348480qt2 [0, 0, 0, -437052, -62844496]  6635520
348480.qt4 348480qt1 [0, 0, 0, -197472, 33083336]  3317760 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 348480.qt have rank $$0$$.

## Modular form 348480.2.a.qt

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} - 4q^{13} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 