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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 6384.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6384.e1 | 6384t3 | \([0, -1, 0, -290424, -60144912]\) | \(661397832743623417/443352042\) | \(1815969964032\) | \([2]\) | \(30720\) | \(1.6684\) | |
| 6384.e2 | 6384t2 | \([0, -1, 0, -18264, -922896]\) | \(164503536215257/4178071044\) | \(17113378996224\) | \([2, 2]\) | \(15360\) | \(1.3219\) | |
| 6384.e3 | 6384t1 | \([0, -1, 0, -2584, 30448]\) | \(466025146777/177366672\) | \(726493888512\) | \([2]\) | \(7680\) | \(0.97530\) | \(\Gamma_0(N)\)-optimal |
| 6384.e4 | 6384t4 | \([0, -1, 0, 3016, -2965776]\) | \(740480746823/927484650666\) | \(-3798977129127936\) | \([2]\) | \(30720\) | \(1.6684\) |
Rank
sage: E.rank()
The elliptic curves in class 6384.e have rank \(1\).
Complex multiplication
The elliptic curves in class 6384.e do not have complex multiplication.Modular form 6384.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
