# Properties

 Label 78400.bc Number of curves $2$ Conductor $78400$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 78400.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78400.bc1 78400cy2 $$[0, 1, 0, -1177633, -350227137]$$ $$2185454/625$$ $$51652616960000000000$$ $$[2]$$ $$2064384$$ $$2.4891$$
78400.bc2 78400cy1 $$[0, 1, 0, 194367, -36039137]$$ $$19652/25$$ $$-1033052339200000000$$ $$[2]$$ $$1032192$$ $$2.1426$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 78400.bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 78400.bc do not have complex multiplication.

## Modular form 78400.2.a.bc

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.