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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 305760.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 305760.dn1 | 305760dn2 | \([0, -1, 0, -61560, 5898600]\) | \(428320044872/73125\) | \(4404778560000\) | \([2]\) | \(884736\) | \(1.4327\) | |
| 305760.dn2 | 305760dn4 | \([0, -1, 0, -26280, -1575468]\) | \(33324076232/1285245\) | \(77418387970560\) | \([2]\) | \(884736\) | \(1.4327\) | |
| 305760.dn3 | 305760dn1 | \([0, -1, 0, -4230, 73872]\) | \(1111934656/342225\) | \(2576795457600\) | \([2, 2]\) | \(442368\) | \(1.0861\) | \(\Gamma_0(N)\)-optimal |
| 305760.dn4 | 305760dn3 | \([0, -1, 0, 11695, 484737]\) | \(367061696/426465\) | \(-205509348495360\) | \([2]\) | \(884736\) | \(1.4327\) |
Rank
sage: E.rank()
The elliptic curves in class 305760.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 305760.dn do not have complex multiplication.Modular form 305760.2.a.dn
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.
