# Properties

 Label 1078.e Number of curves $2$ Conductor $1078$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 1078.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1078.e1 1078a2 $$[1, 0, 1, -271, -1718]$$ $$911871625/10648$$ $$25565848$$ $$[]$$ $$288$$ $$0.23367$$
1078.e2 1078a1 $$[1, 0, 1, -26, 46]$$ $$765625/22$$ $$52822$$ $$$$ $$96$$ $$-0.31563$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1078.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1078.e do not have complex multiplication.

## Modular form1078.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} - 2 q^{9} - q^{11} + q^{12} - q^{13} + q^{16} - 6 q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})$$ ## 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. 