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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 111090w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111090.x3 | 111090w1 | \([1, 0, 1, -116487134, -483919968304]\) | \(1180838681727016392361/692428800000\) | \(102504312977203200000\) | \([2]\) | \(16220160\) | \(3.1638\) | \(\Gamma_0(N)\)-optimal |
| 111090.x2 | 111090w2 | \([1, 0, 1, -117164254, -478009523248]\) | \(1201550658189465626281/28577902500000000\) | \(4230555202342822500000000\) | \([2, 2]\) | \(32440320\) | \(3.5104\) | |
| 111090.x4 | 111090w3 | \([1, 0, 1, 15085746, -1496122923248]\) | \(2564821295690373719/6533572090396050000\) | \(-967203152747367623838450000\) | \([2]\) | \(64880640\) | \(3.8570\) | |
| 111090.x1 | 111090w4 | \([1, 0, 1, -260248174, 918375068816]\) | \(13167998447866683762601/5158996582031250000\) | \(763716645368957519531250000\) | \([2]\) | \(64880640\) | \(3.8570\) |
Rank
sage: E.rank()
The elliptic curves in class 111090w have rank \(1\).
Complex multiplication
The elliptic curves in class 111090w do not have complex multiplication.Modular form 111090.2.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.
