# Properties

 Label 211420m Number of curves 4 Conductor 211420 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("211420.n1")

sage: E.isogeny_class()

## Elliptic curves in class 211420m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
211420.n4 211420m1 [0, -1, 0, -43565, -3413650] [2] 1036800 $$\Gamma_0(N)$$-optimal
211420.n3 211420m2 [0, -1, 0, -96420, 6544232] [2] 2073600
211420.n2 211420m3 [0, -1, 0, -427965, 106543970] [2] 3110400
211420.n1 211420m4 [0, -1, 0, -6823420, 6862702632] [2] 6220800

## Rank

sage: E.rank()

The elliptic curves in class 211420m have rank $$1$$.

## Modular form 211420.2.a.n

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} - 4q^{7} + q^{9} + q^{11} + 4q^{13} + 2q^{15} - 4q^{19} + O(q^{20})$$

## 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.