# Properties

 Label 4900.i Number of curves $2$ Conductor $4900$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4900.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4900.i1 4900b1 $$[0, -1, 0, -24908, 1522312]$$ $$-177953104/125$$ $$-1200500000000$$ $$[]$$ $$10368$$ $$1.2541$$ $$\Gamma_0(N)$$-optimal
4900.i2 4900b2 $$[0, -1, 0, 24092, 6422312]$$ $$161017136/1953125$$ $$-18757812500000000$$ $$[]$$ $$31104$$ $$1.8034$$

## Rank

sage: E.rank()

The elliptic curves in class 4900.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4900.i do not have complex multiplication.

## Modular form4900.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} - 2 q^{9} + 6 q^{11} - 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 