# Properties

 Label 72450.s Number of curves $2$ Conductor $72450$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 72450.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.s1 72450k2 $$[1, -1, 0, -505617, 138504041]$$ $$371850068871/14812$$ $$569423039062500$$ $$$$ $$675840$$ $$1.9145$$
72450.s2 72450k1 $$[1, -1, 0, -33117, 1951541]$$ $$104487111/18032$$ $$693210656250000$$ $$$$ $$337920$$ $$1.5679$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 72450.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 72450.s do not have complex multiplication.

## Modular form 72450.2.a.s

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} + 6q^{13} + q^{14} + q^{16} + 6q^{19} + O(q^{20})$$ ## 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. 