# Properties

 Label 61347l Number of curves $2$ Conductor $61347$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 61347l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61347.g2 61347l1 $$[1, 1, 1, 40472, -3939616]$$ $$857375/1287$$ $$-11005119726978663$$ $$$$ $$322560$$ $$1.7635$$ $$\Gamma_0(N)$$-optimal
61347.g1 61347l2 $$[1, 1, 1, -266263, -39888958]$$ $$244140625/61347$$ $$524577373652649603$$ $$$$ $$645120$$ $$2.1101$$

## Rank

sage: E.rank()

The elliptic curves in class 61347l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 61347l do not have complex multiplication.

## Modular form 61347.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} + q^{6} + 3q^{8} + q^{9} + q^{12} - q^{16} + 4q^{17} - q^{18} - 8q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 