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SageMath
E = EllipticCurve("dh1")
E.isogeny_class()
Elliptic curves in class 162288.dh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.dh1 | 162288fe2 | \([0, 0, 0, -7483035, -1148735126]\) | \(263822189935250/149429406721\) | \(26247128223316990445568\) | \([2]\) | \(8847360\) | \(2.9918\) | |
| 162288.dh2 | 162288fe1 | \([0, 0, 0, 1848525, -142792958]\) | \(7953970437500/4703287687\) | \(-413063926641717378048\) | \([2]\) | \(4423680\) | \(2.6452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162288.dh have rank \(0\).
Complex multiplication
The elliptic curves in class 162288.dh do not have complex multiplication.Modular form 162288.2.a.dh
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
