# Properties

 Label 7920ba Number of curves 4 Conductor 7920 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7920.o1")

sage: E.isogeny_class()

## Elliptic curves in class 7920ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7920.o4 7920ba1 [0, 0, 0, -408, 3107] [2] 3456 $$\Gamma_0(N)$$-optimal
7920.o3 7920ba2 [0, 0, 0, -903, -5902] [2] 6912
7920.o2 7920ba3 [0, 0, 0, -4008, -96433] [2] 10368
7920.o1 7920ba4 [0, 0, 0, -63903, -6217702] [2] 20736

## Rank

sage: E.rank()

The elliptic curves in class 7920ba have rank $$1$$.

## Modular form7920.2.a.o

sage: E.q_eigenform(10)

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

## 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 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.