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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 101430.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.ep1 | 101430fh2 | \([1, -1, 1, -4047287, 732305711]\) | \(85486955243540761/46777901234400\) | \(4011959137395599762400\) | \([2]\) | \(4915200\) | \(2.8360\) | |
| 101430.ep2 | 101430fh1 | \([1, -1, 1, -2424407, -1443002641]\) | \(18374873741826841/136564270080\) | \(11712587711957959680\) | \([2]\) | \(2457600\) | \(2.4895\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101430.ep have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.ep do not have complex multiplication.Modular form 101430.2.a.ep
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.
