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SageMath
E = EllipticCurve("nw1")
E.isogeny_class()
Elliptic curves in class 348480.nw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348480.nw1 | 348480nw5 | \([0, 0, 0, -11923941612, 501161691323216]\) | \(553808571467029327441/12529687500\) | \(4241932961141145600000000\) | \([2]\) | \(283115520\) | \(4.2497\) | |
| 348480.nw2 | 348480nw4 | \([0, 0, 0, -824156652, -9086792135344]\) | \(182864522286982801/463015182960\) | \(156754058399846133462466560\) | \([2]\) | \(141557760\) | \(3.9032\) | |
| 348480.nw3 | 348480nw3 | \([0, 0, 0, -746097132, 7811876216144]\) | \(135670761487282321/643043610000\) | \(217702786658501418024960000\) | \([2, 2]\) | \(141557760\) | \(3.9032\) | |
| 348480.nw4 | 348480nw6 | \([0, 0, 0, -362769132, 15828491345744]\) | \(-15595206456730321/310672490129100\) | \(-105178351495073320087820697600\) | \([2]\) | \(283115520\) | \(4.2497\) | |
| 348480.nw5 | 348480nw2 | \([0, 0, 0, -71439852, -21974256304]\) | \(119102750067601/68309049600\) | \(23126068311158230194585600\) | \([2, 2]\) | \(70778880\) | \(3.5566\) | |
| 348480.nw6 | 348480nw1 | \([0, 0, 0, 17771028, -2740390576]\) | \(1833318007919/1070530560\) | \(-362428741209458642780160\) | \([2]\) | \(35389440\) | \(3.2100\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348480.nw have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.nw do not have complex multiplication.Modular form 348480.2.a.nw
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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
