# Properties

 Label 62475.cm Number of curves 4 Conductor 62475 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("62475.cm1")

sage: E.isogeny_class()

## Elliptic curves in class 62475.cm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62475.cm1 62475bs4 [1, 0, 1, -2065376, -1142597977]  1179648
62475.cm2 62475bs3 [1, 0, 1, -656626, 190324523]  1179648
62475.cm3 62475bs2 [1, 0, 1, -136001, -15842977] [2, 2] 589824
62475.cm4 62475bs1 [1, 0, 1, 17124, -1449227]  294912 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 62475.cm have rank $$1$$.

## Modular form 62475.2.a.cm

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 