# Properties

 Label 8036.c Number of curves $2$ Conductor $8036$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8036.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8036.c1 8036f1 $$[0, -1, 0, -44, -104]$$ $$-768208/41$$ $$-514304$$ $$[]$$ $$1152$$ $$-0.14519$$ $$\Gamma_0(N)$$-optimal
8036.c2 8036f2 $$[0, -1, 0, 236, -328]$$ $$115393712/68921$$ $$-864545024$$ $$[]$$ $$3456$$ $$0.40411$$

## Rank

sage: E.rank()

The elliptic curves in class 8036.c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8036.c do not have complex multiplication.

## Modular form8036.2.a.c

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 