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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 90354q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90354.p4 | 90354q1 | \([1, 1, 1, -31194747, 57821093769]\) | \(1308451928740468777/194033737531392\) | \(497837484621266920931328\) | \([2]\) | \(21012480\) | \(3.2716\) | \(\Gamma_0(N)\)-optimal |
| 90354.p2 | 90354q2 | \([1, 1, 1, -479788667, 4044744417161]\) | \(4760617885089919932457/133756441657344\) | \(343182434734115229597696\) | \([2, 2]\) | \(42024960\) | \(3.6182\) | |
| 90354.p3 | 90354q3 | \([1, 1, 1, -460513147, 4384648936841]\) | \(-4209586785160189454377/801182513521564416\) | \(-2055615133371277413125862144\) | \([2]\) | \(84049920\) | \(3.9648\) | |
| 90354.p1 | 90354q4 | \([1, 1, 1, -7676566907, 258876904472969]\) | \(19499096390516434897995817/15393430272\) | \(39495330573970453248\) | \([2]\) | \(84049920\) | \(3.9648\) |
Rank
sage: E.rank()
The elliptic curves in class 90354q have rank \(1\).
Complex multiplication
The elliptic curves in class 90354q do not have complex multiplication.Modular form 90354.2.a.q
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.
