# Properties

 Label 97104.bc Number of curves $4$ Conductor $97104$ CM no Rank $2$ Graph

# Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 97104.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97104.bc1 97104bi4 $$[0, -1, 0, -23485392, -43799289408]$$ $$14489843500598257/6246072$$ $$617533414928252928$$ $$[2]$$ $$5308416$$ $$2.7563$$
97104.bc2 97104bi3 $$[0, -1, 0, -3139792, 1132969408]$$ $$34623662831857/14438442312$$ $$1427492444399286386688$$ $$[2]$$ $$5308416$$ $$2.7563$$
97104.bc3 97104bi2 $$[0, -1, 0, -1475152, -676827200]$$ $$3590714269297/73410624$$ $$7257923592736997376$$ $$[2, 2]$$ $$2654208$$ $$2.4097$$
97104.bc4 97104bi1 $$[0, -1, 0, 4528, -31686720]$$ $$103823/4386816$$ $$-433713454654685184$$ $$[2]$$ $$1327104$$ $$2.0632$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 97104.bc have rank $$2$$.

## Complex multiplication

The elliptic curves in class 97104.bc do not have complex multiplication.

## Modular form 97104.2.a.bc

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - q^{7} + q^{9} - 6q^{13} - 2q^{15} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.