# Properties

 Label 7260n Number of curves $4$ Conductor $7260$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 7260n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7260.l4 7260n1 $$[0, 1, 0, 26459, 6095384]$$ $$72268906496/606436875$$ $$-17189438667390000$$ $$$$ $$34560$$ $$1.7966$$ $$\Gamma_0(N)$$-optimal
7260.l3 7260n2 $$[0, 1, 0, -381916, 83523284]$$ $$13584145739344/1195803675$$ $$542320423497388800$$ $$$$ $$69120$$ $$2.1432$$
7260.l2 7260n3 $$[0, 1, 0, -1890181, 1000400300]$$ $$-26348629355659264/24169921875$$ $$-685095855468750000$$ $$$$ $$103680$$ $$2.3459$$
7260.l1 7260n4 $$[0, 1, 0, -30249556, 64026275300]$$ $$6749703004355978704/5671875$$ $$2572306572000000$$ $$$$ $$207360$$ $$2.6925$$

## Rank

sage: E.rank()

The elliptic curves in class 7260n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 7260n do not have complex multiplication.

## Modular form7260.2.a.n

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2q^{7} + q^{9} - 2q^{13} - q^{15} - 2q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 