# Properties

 Label 115920.dc Number of curves $4$ Conductor $115920$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dc1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dc1 115920ej4 $$[0, 0, 0, -434110827, 9550427546]$$ $$3029968325354577848895529/1753440696000000000000$$ $$5235745863204864000000000000$$ $$$$ $$53084160$$ $$4.0082$$
115920.dc2 115920ej2 $$[0, 0, 0, -298633467, 1986339218474]$$ $$986396822567235411402169/6336721794060000$$ $$18921349889514455040000$$ $$$$ $$17694720$$ $$3.4589$$
115920.dc3 115920ej1 $$[0, 0, 0, -18305787, 32287092266]$$ $$-227196402372228188089/19338934824115200$$ $$-57745749961850801356800$$ $$$$ $$8847360$$ $$3.1124$$ $$\Gamma_0(N)$$-optimal
115920.dc4 115920ej3 $$[0, 0, 0, 108527253, 1193801114]$$ $$47342661265381757089751/27397579603968000000$$ $$-81808734336174784512000000$$ $$$$ $$26542080$$ $$3.6617$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.dc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 115920.dc do not have complex multiplication.

## Modular form 115920.2.a.dc

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - 4q^{13} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 