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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 27930b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27930.f3 | 27930b1 | \([1, 1, 0, -1103, -174747]\) | \(-1263214441/110808000\) | \(-13036450392000\) | \([2]\) | \(51840\) | \(1.1962\) | \(\Gamma_0(N)\)-optimal |
| 27930.f2 | 27930b2 | \([1, 1, 0, -54023, -4821123]\) | \(148212258825961/1218375000\) | \(143340600375000\) | \([2]\) | \(103680\) | \(1.5427\) | |
| 27930.f4 | 27930b3 | \([1, 1, 0, 9922, 4682868]\) | \(918046641959/80912056320\) | \(-9519222513991680\) | \([2]\) | \(155520\) | \(1.7455\) | |
| 27930.f1 | 27930b4 | \([1, 1, 0, -366398, 82280052]\) | \(46237740924063961/1806561830400\) | \(212540192784729600\) | \([2]\) | \(311040\) | \(2.0921\) |
Rank
sage: E.rank()
The elliptic curves in class 27930b have rank \(0\).
Complex multiplication
The elliptic curves in class 27930b do not have complex multiplication.Modular form 27930.2.a.b
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.
