# Properties

 Label 372810.i Number of curves $2$ Conductor $372810$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 372810.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372810.i1 372810i2 $$[1, 1, 0, -68643, -6729723]$$ $$1481933914201/53916840$$ $$1301421445761960$$ $$$$ $$2838528$$ $$1.6699$$
372810.i2 372810i1 $$[1, 1, 0, -10843, 287197]$$ $$5841725401/1857600$$ $$44837948174400$$ $$$$ $$1419264$$ $$1.3233$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 372810.i have rank $$1$$.

## Complex multiplication

The elliptic curves in class 372810.i do not have complex multiplication.

## Modular form 372810.2.a.i

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} + 2q^{11} - q^{12} - 2q^{13} - 2q^{14} + q^{15} + q^{16} - q^{18} - 6q^{19} + O(q^{20})$$ ## 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. 