# Properties

 Label 30420j Number of curves 4 Conductor 30420 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30420.c1")

sage: E.isogeny_class()

## Elliptic curves in class 30420j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30420.c3 30420j1 [0, 0, 0, -2028, -24167]  27648 $$\Gamma_0(N)$$-optimal
30420.c4 30420j2 [0, 0, 0, 5577, -162578]  55296
30420.c1 30420j3 [0, 0, 0, -62868, 6065917]  82944
30420.c2 30420j4 [0, 0, 0, -55263, 7588438]  165888

## Rank

sage: E.rank()

The elliptic curves in class 30420j have rank $$1$$.

## Modular form 30420.2.a.c

sage: E.q_eigenform(10)

$$q - q^{5} - 2q^{7} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 