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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 302016x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.x4 | 302016x1 | \([0, -1, 0, 42431, -75218207]\) | \(18191447/5271552\) | \(-2448130292494368768\) | \([2]\) | \(4423680\) | \(2.2076\) | \(\Gamma_0(N)\)-optimal |
| 302016.x3 | 302016x2 | \([0, -1, 0, -2435649, -1422798111]\) | \(3440899317673/106007616\) | \(49230370100628946944\) | \([2, 2]\) | \(8847360\) | \(2.5542\) | |
| 302016.x2 | 302016x3 | \([0, -1, 0, -5843009, 3440867553]\) | \(47504791830313/16490207448\) | \(7658119730767155167232\) | \([2]\) | \(17694720\) | \(2.9008\) | |
| 302016.x1 | 302016x4 | \([0, -1, 0, -38677569, -92571226911]\) | \(13778603383488553/13703976\) | \(6364182459589853184\) | \([2]\) | \(17694720\) | \(2.9008\) |
Rank
sage: E.rank()
The elliptic curves in class 302016x have rank \(1\).
Complex multiplication
The elliptic curves in class 302016x do not have complex multiplication.Modular form 302016.2.a.x
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.
