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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 291312.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 291312.be1 | 291312be3 | \([0, 0, 0, -211368531, 1182792182546]\) | \(14489843500598257/6246072\) | \(450181859482696384512\) | \([2]\) | \(42467328\) | \(3.3056\) | |
| 291312.be2 | 291312be4 | \([0, 0, 0, -28258131, -30561915886]\) | \(34623662831857/14438442312\) | \(1040641991967079775895552\) | \([2]\) | \(42467328\) | \(3.3056\) | |
| 291312.be3 | 291312be2 | \([0, 0, 0, -13276371, 18287610770]\) | \(3590714269297/73410624\) | \(5291026299105271087104\) | \([2, 2]\) | \(21233664\) | \(2.9590\) | |
| 291312.be4 | 291312be1 | \([0, 0, 0, 40749, 855500690]\) | \(103823/4386816\) | \(-316177108443265499136\) | \([2]\) | \(10616832\) | \(2.6125\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 291312.be have rank \(1\).
Complex multiplication
The elliptic curves in class 291312.be do not have complex multiplication.Modular form 291312.2.a.be
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.
