# Properties

 Label 1323.l Number of curves $3$ Conductor $1323$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 1323.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1323.l1 1323c3 $$[0, 0, 1, -187866, 31341539]$$ $$35184082944/7$$ $$145888171821$$ $$[]$$ $$5184$$ $$1.5316$$
1323.l2 1323c2 $$[0, 0, 1, -2646, 30098]$$ $$884736/343$$ $$794280046581$$ $$[]$$ $$1728$$ $$0.98228$$
1323.l3 1323c1 $$[0, 0, 1, -1176, -15521]$$ $$56623104/7$$ $$22235661$$ $$[]$$ $$576$$ $$0.43298$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1323.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1323.l do not have complex multiplication.

## Modular form1323.2.a.l

sage: E.q_eigenform(10)

$$q - 2q^{4} + 3q^{5} - 6q^{11} + 4q^{13} + 4q^{16} + 3q^{17} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 