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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 46410f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.g4 | 46410f1 | \([1, 1, 0, -6246123, 20452740477]\) | \(-26949791983733109138764089/165161952797784563712000\) | \(-165161952797784563712000\) | \([2]\) | \(6488064\) | \(3.1388\) | \(\Gamma_0(N)\)-optimal |
| 46410.g3 | 46410f2 | \([1, 1, 0, -156836843, 754401791613]\) | \(426646307804307769001905914169/998470877001641316000000\) | \(998470877001641316000000\) | \([2, 2]\) | \(12976128\) | \(3.4853\) | |
| 46410.g2 | 46410f3 | \([1, 1, 0, -215146843, 142578285613]\) | \(1101358349464662961278219354169/628567168199833707765102000\) | \(628567168199833707765102000\) | \([2]\) | \(25952256\) | \(3.8319\) | |
| 46410.g1 | 46410f4 | \([1, 1, 0, -2507978363, 48341976384717]\) | \(1744596788171434949302427839201849/9588363813082031250000\) | \(9588363813082031250000\) | \([2]\) | \(25952256\) | \(3.8319\) |
Rank
sage: E.rank()
The elliptic curves in class 46410f have rank \(0\).
Complex multiplication
The elliptic curves in class 46410f do not have complex multiplication.Modular form 46410.2.a.f
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
