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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 282576.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 282576.i1 | 282576i4 | \([0, -1, 0, -2753420824, -55609608153680]\) | \(947531277805646290177/38367\) | \(93477217717481472\) | \([2]\) | \(82575360\) | \(3.6675\) | |
| 282576.i2 | 282576i5 | \([0, -1, 0, -571463144, 4274617393200]\) | \(8471112631466271697/1662662681263647\) | \(4050905242714140611017469952\) | \([2]\) | \(165150720\) | \(4.0140\) | |
| 282576.i3 | 282576i3 | \([0, -1, 0, -175385784, -833829965136]\) | \(244883173420511137/18418027974129\) | \(44873615629690117580427264\) | \([2, 2]\) | \(82575360\) | \(3.6675\) | |
| 282576.i4 | 282576i2 | \([0, -1, 0, -172089064, -868854318416]\) | \(231331938231569617/1472026689\) | \(3586440412166611636224\) | \([2, 2]\) | \(41287680\) | \(3.3209\) | |
| 282576.i5 | 282576i1 | \([0, -1, 0, -10549784, -14117680080]\) | \(-53297461115137/4513839183\) | \(-10997501187243977699328\) | \([2]\) | \(20643840\) | \(2.9743\) | \(\Gamma_0(N)\)-optimal |
| 282576.i6 | 282576i6 | \([0, -1, 0, 167944056, -3700771461072]\) | \(215015459663151503/2552757445339983\) | \(-6219528852867500696139952128\) | \([2]\) | \(165150720\) | \(4.0140\) |
Rank
sage: E.rank()
The elliptic curves in class 282576.i have rank \(0\).
Complex multiplication
The elliptic curves in class 282576.i do not have complex multiplication.Modular form 282576.2.a.i
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
