# Properties

 Label 11310.f Number of curves $2$ Conductor $11310$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 11310.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11310.f1 11310f1 $$[1, 0, 1, -833, 7796]$$ $$63812982460681/10201800960$$ $$10201800960$$ $$$$ $$7680$$ $$0.64290$$ $$\Gamma_0(N)$$-optimal
11310.f2 11310f2 $$[1, 0, 1, 1487, 43988]$$ $$363979050334199/1041836936400$$ $$-1041836936400$$ $$$$ $$15360$$ $$0.98947$$

## Rank

sage: E.rank()

The elliptic curves in class 11310.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 11310.f do not have complex multiplication.

## Modular form 11310.2.a.f

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} - q^{13} + q^{15} + q^{16} - 4 q^{17} - q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 