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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 183456.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 183456.dd1 | 183456dj1 | \([0, 0, 0, -1279929, 557184292]\) | \(42246001231552/14414517\) | \(79121741387427648\) | \([2]\) | \(2211840\) | \(2.2141\) | \(\Gamma_0(N)\)-optimal |
| 183456.dd2 | 183456dj2 | \([0, 0, 0, -1101324, 718214560]\) | \(-420526439488/390971529\) | \(-137347528555597860864\) | \([2]\) | \(4423680\) | \(2.5606\) |
Rank
sage: E.rank()
The elliptic curves in class 183456.dd have rank \(0\).
Complex multiplication
The elliptic curves in class 183456.dd do not have complex multiplication.Modular form 183456.2.a.dd
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.
