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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 230115w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230115.w4 | 230115w1 | \([1, 1, 0, 22472, -2402477]\) | \(8477185319/21880935\) | \(-3239163664876215\) | \([2]\) | \(1013760\) | \(1.6599\) | \(\Gamma_0(N)\)-optimal |
| 230115.w3 | 230115w2 | \([1, 1, 0, -191773, -27212048]\) | \(5268932332201/900900225\) | \(133365565708175025\) | \([2, 2]\) | \(2027520\) | \(2.0065\) | |
| 230115.w2 | 230115w3 | \([1, 1, 0, -882118, 292969963]\) | \(512787603508921/45649063125\) | \(6757699641726493125\) | \([2]\) | \(4055040\) | \(2.3531\) | |
| 230115.w1 | 230115w4 | \([1, 1, 0, -2929348, -1930921703]\) | \(18778886261717401/732035835\) | \(108367575614082315\) | \([2]\) | \(4055040\) | \(2.3531\) |
Rank
sage: E.rank()
The elliptic curves in class 230115w have rank \(1\).
Complex multiplication
The elliptic curves in class 230115w do not have complex multiplication.Modular form 230115.2.a.w
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.
