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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 185130.eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.eb1 | 185130bk2 | \([1, -1, 1, -958343, 328842231]\) | \(75370704203521/7497765000\) | \(9683123336589285000\) | \([2]\) | \(4423680\) | \(2.3796\) | |
| 185130.eb2 | 185130bk1 | \([1, -1, 1, -217823, -33420153]\) | \(885012508801/137332800\) | \(177360912293083200\) | \([2]\) | \(2211840\) | \(2.0330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185130.eb have rank \(1\).
Complex multiplication
The elliptic curves in class 185130.eb do not have complex multiplication.Modular form 185130.2.a.eb
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.
