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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 355740bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 355740.bv4 | 355740bv1 | \([0, -1, 0, 1296475, -2088123750]\) | \(72268906496/606436875\) | \(-2022320269779766110000\) | \([2]\) | \(12441600\) | \(2.7696\) | \(\Gamma_0(N)\)-optimal |
| 355740.bv3 | 355740bv2 | \([0, -1, 0, -18713900, -28685914200]\) | \(13584145739344/1195803675\) | \(63803455504044294931200\) | \([2]\) | \(24883200\) | \(3.1161\) | |
| 355740.bv2 | 355740bv3 | \([0, -1, 0, -92618885, -343322540658]\) | \(-26348629355659264/24169921875\) | \(-80600842300042968750000\) | \([2]\) | \(37324800\) | \(3.3189\) | |
| 355740.bv1 | 355740bv4 | \([0, -1, 0, -1482228260, -21963976884408]\) | \(6749703004355978704/5671875\) | \(302629295889228000000\) | \([2]\) | \(74649600\) | \(3.6655\) |
Rank
sage: E.rank()
The elliptic curves in class 355740bv have rank \(1\).
Complex multiplication
The elliptic curves in class 355740bv do not have complex multiplication.Modular form 355740.2.a.bv
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
