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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 146523.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 146523.y1 | 146523s6 | \([1, 0, 1, -985319352, -11902817825819]\) | \(908031902324522977/161726530797\) | \(18842343321074404250124837\) | \([2]\) | \(49545216\) | \(3.8542\) | |
| 146523.y2 | 146523s4 | \([1, 0, 1, -67841167, -145885371955]\) | \(296380748763217/92608836489\) | \(10789618024276259223855969\) | \([2, 2]\) | \(24772608\) | \(3.5077\) | |
| 146523.y3 | 146523s2 | \([1, 0, 1, -26570522, 50975604695]\) | \(17806161424897/668584449\) | \(77895059425976667471129\) | \([2, 2]\) | \(12386304\) | \(3.1611\) | |
| 146523.y4 | 146523s1 | \([1, 0, 1, -26326317, 51989348491]\) | \(17319700013617/25857\) | \(3012532754224259097\) | \([2]\) | \(6193152\) | \(2.8145\) | \(\Gamma_0(N)\)-optimal |
| 146523.y5 | 146523s3 | \([1, 0, 1, 10792843, 182957955221]\) | \(1193377118543/124806800313\) | \(-14540920210884441827731473\) | \([2]\) | \(24772608\) | \(3.5077\) | |
| 146523.y6 | 146523s5 | \([1, 0, 1, 189306698, -987890341111]\) | \(6439735268725823/7345472585373\) | \(-855802171895135276956955733\) | \([2]\) | \(49545216\) | \(3.8542\) |
Rank
sage: E.rank()
The elliptic curves in class 146523.y have rank \(0\).
Complex multiplication
The elliptic curves in class 146523.y do not have complex multiplication.Modular form 146523.2.a.y
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 LMFDB numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
