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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 81120.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81120.w1 | 81120bh4 | \([0, -1, 0, -4330767185, 109698599964225]\) | \(454357982636417669333824/3003024375\) | \(59371622729602560000\) | \([4]\) | \(36126720\) | \(3.8532\) | |
| 81120.w2 | 81120bh3 | \([0, -1, 0, -289242880, 1465479677752]\) | \(1082883335268084577352/251301565117746585\) | \(621048143986905741412999680\) | \([2]\) | \(36126720\) | \(3.8532\) | |
| 81120.w3 | 81120bh1 | \([0, -1, 0, -270678230, 1714038063672]\) | \(7099759044484031233216/577161945398025\) | \(178294430240300521742400\) | \([2, 2]\) | \(18063360\) | \(3.5066\) | \(\Gamma_0(N)\)-optimal |
| 81120.w4 | 81120bh2 | \([0, -1, 0, -252198080, 1958101708692]\) | \(-717825640026599866952/254764560814329735\) | \(-629606336010062896059194880\) | \([2]\) | \(36126720\) | \(3.8532\) |
Rank
sage: E.rank()
The elliptic curves in class 81120.w have rank \(1\).
Complex multiplication
The elliptic curves in class 81120.w do not have complex multiplication.Modular form 81120.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
