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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 290145u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 290145.u4 | 290145u1 | \([1, 1, 0, 7552, -15117]\) | \(80062991/46575\) | \(-27703896175575\) | \([2]\) | \(967680\) | \(1.2688\) | \(\Gamma_0(N)\)-optimal |
| 290145.u3 | 290145u2 | \([1, 1, 0, -30293, -158928]\) | \(5168743489/2975625\) | \(1769971144550625\) | \([2, 2]\) | \(1935360\) | \(1.6154\) | |
| 290145.u2 | 290145u3 | \([1, 1, 0, -320438, 69417843]\) | \(6117442271569/26953125\) | \(16032347323828125\) | \([2]\) | \(3870720\) | \(1.9620\) | |
| 290145.u1 | 290145u4 | \([1, 1, 0, -345668, -78182703]\) | \(7679186557489/20988075\) | \(12484196472897075\) | \([2]\) | \(3870720\) | \(1.9620\) |
Rank
sage: E.rank()
The elliptic curves in class 290145u have rank \(1\).
Complex multiplication
The elliptic curves in class 290145u do not have complex multiplication.Modular form 290145.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
