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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 3120f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3120.i4 | 3120f1 | \([0, -1, 0, -2295, 36450]\) | \(83587439220736/13990184325\) | \(223842949200\) | \([2]\) | \(3072\) | \(0.89895\) | \(\Gamma_0(N)\)-optimal |
| 3120.i2 | 3120f2 | \([0, -1, 0, -35100, 2542752]\) | \(18681746265374416/693005625\) | \(177409440000\) | \([2, 2]\) | \(6144\) | \(1.2455\) | |
| 3120.i1 | 3120f3 | \([0, -1, 0, -561600, 162177552]\) | \(19129597231400697604/26325\) | \(26956800\) | \([4]\) | \(12288\) | \(1.5921\) | |
| 3120.i3 | 3120f4 | \([0, -1, 0, -33480, 2786400]\) | \(-4053153720264484/903687890625\) | \(-925376400000000\) | \([4]\) | \(12288\) | \(1.5921\) |
Rank
sage: E.rank()
The elliptic curves in class 3120f have rank \(1\).
Complex multiplication
The elliptic curves in class 3120f do not have complex multiplication.Modular form 3120.2.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.
