# Properties

 Label 1296.a Number of curves $2$ Conductor $1296$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 1296.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1296.a1 1296i1 $$[0, 0, 0, -39, -94]$$ $$-316368$$ $$-20736$$ $$[]$$ $$144$$ $$-0.30456$$ $$\Gamma_0(N)$$-optimal
1296.a2 1296i2 $$[0, 0, 0, 81, -486]$$ $$432$$ $$-136048896$$ $$[]$$ $$432$$ $$0.24475$$

## Rank

sage: E.rank()

The elliptic curves in class 1296.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1296.a do not have complex multiplication.

## Modular form1296.2.a.a

sage: E.q_eigenform(10)

$$q - 3 q^{5} - 2 q^{7} - 6 q^{11} + 5 q^{13} + 3 q^{17} - 2 q^{19} + O(q^{20})$$

## 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. 