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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 87120.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.g1 | 87120dd3 | \([0, 0, 0, -187032483, -984516180318]\) | \(5066026756449723/11000000\) | \(1571086281904128000000\) | \([2]\) | \(14929920\) | \(3.3140\) | |
| 87120.g2 | 87120dd4 | \([0, 0, 0, -184941603, -1007603259102]\) | \(-4898016158612283/236328125000\) | \(-33753806837784000000000000\) | \([2]\) | \(29859840\) | \(3.6606\) | |
| 87120.g3 | 87120dd1 | \([0, 0, 0, -3035043, -431086942]\) | \(15781142246787/8722841600\) | \(1708983261875876659200\) | \([2]\) | \(4976640\) | \(2.7647\) | \(\Gamma_0(N)\)-optimal |
| 87120.g4 | 87120dd2 | \([0, 0, 0, 11833437, -3407756638]\) | \(935355271080573/566899520000\) | \(-111067222732265226240000\) | \([2]\) | \(9953280\) | \(3.1113\) |
Rank
sage: E.rank()
The elliptic curves in class 87120.g have rank \(1\).
Complex multiplication
The elliptic curves in class 87120.g do not have complex multiplication.Modular form 87120.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
