# Properties

 Label 6300.p Number of curves 4 Conductor 6300 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6300.p1")

sage: E.isogeny_class()

## Elliptic curves in class 6300.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6300.p1 6300j4 [0, 0, 0, -411375, 101555750]  41472
6300.p2 6300j3 [0, 0, 0, -25500, 1614125]  20736
6300.p3 6300j2 [0, 0, 0, -6375, 62750]  13824
6300.p4 6300j1 [0, 0, 0, 1500, 7625]  6912 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6300.p have rank $$1$$.

## Modular form6300.2.a.p

sage: E.q_eigenform(10)

$$q - q^{7} + 6q^{11} - 2q^{13} - 4q^{19} + O(q^{20})$$

## 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. 