# Properties

 Label 23100bc Number of curves $2$ Conductor $23100$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 23100bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23100.bh2 23100bc1 $$[0, 1, 0, -533, 14688]$$ $$-67108864/343035$$ $$-85758750000$$ $$$$ $$23040$$ $$0.78222$$ $$\Gamma_0(N)$$-optimal
23100.bh1 23100bc2 $$[0, 1, 0, -12908, 559188]$$ $$59466754384/121275$$ $$485100000000$$ $$$$ $$46080$$ $$1.1288$$

## Rank

sage: E.rank()

The elliptic curves in class 23100bc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 23100bc do not have complex multiplication.

## Modular form 23100.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + q^{11} + 6q^{13} - 2q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 