# Properties

 Label 31200.e Number of curves $2$ Conductor $31200$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 31200.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.e1 31200g2 $$[0, -1, 0, -830408, -290974188]$$ $$7916055336451592/385003125$$ $$3080025000000000$$ $$$$ $$276480$$ $$2.0444$$
31200.e2 31200g1 $$[0, -1, 0, -49158, -5036688]$$ $$-13137573612736/3427734375$$ $$-3427734375000000$$ $$$$ $$138240$$ $$1.6979$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 31200.e have rank $$0$$.

## Complex multiplication

The elliptic curves in class 31200.e do not have complex multiplication.

## Modular form 31200.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} + q^{13} - 6q^{19} + O(q^{20})$$ ## 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. 