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SageMath
sage: E = EllipticCurve("f1")
sage: E.isogeny_class()
Elliptic curves in class 62400.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.f1 | 62400bi4 | \([0, -1, 0, -832033, 292395937]\) | \(31103978031362/195\) | \(399360000000\) | \([4]\) | \(589824\) | \(1.8317\) | |
| 62400.f2 | 62400bi3 | \([0, -1, 0, -72033, 755937]\) | \(20183398562/11567205\) | \(23689635840000000\) | \([2]\) | \(589824\) | \(1.8317\) | |
| 62400.f3 | 62400bi2 | \([0, -1, 0, -52033, 4575937]\) | \(15214885924/38025\) | \(38937600000000\) | \([2, 2]\) | \(294912\) | \(1.4851\) | |
| 62400.f4 | 62400bi1 | \([0, -1, 0, -2033, 125937]\) | \(-3631696/24375\) | \(-6240000000000\) | \([2]\) | \(147456\) | \(1.1385\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62400.f have rank \(2\).
Complex multiplication
The elliptic curves in class 62400.f do not have complex multiplication.Modular form 62400.2.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 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.
