# Properties

 Label 372232.e Number of curves $2$ Conductor $372232$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 372232.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372232.e1 372232e2 $$[0, 1, 0, -141128, 20357920]$$ $$12576878500/1127$$ $$27855913229312$$ $$$$ $$1658880$$ $$1.6199$$
372232.e2 372232e1 $$[0, 1, 0, -8188, 363744]$$ $$-9826000/3703$$ $$-22881643009792$$ $$$$ $$829440$$ $$1.2733$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 372232.e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 372232.e do not have complex multiplication.

## Modular form 372232.2.a.e

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} - 4q^{11} + 6q^{13} + O(q^{20})$$ ## 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. 