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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1155m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1155.f6 | 1155m1 | \([1, 0, 0, 35, -23128]\) | \(4733169839/231139696095\) | \(-231139696095\) | \([4]\) | \(960\) | \(0.85942\) | \(\Gamma_0(N)\)-optimal |
| 1155.f5 | 1155m2 | \([1, 0, 0, -11970, -496125]\) | \(189674274234120481/3859869269025\) | \(3859869269025\) | \([2, 4]\) | \(1920\) | \(1.2060\) | |
| 1155.f2 | 1155m3 | \([1, 0, 0, -190575, -32037768]\) | \(765458482133960722801/326869475625\) | \(326869475625\) | \([2, 2]\) | \(3840\) | \(1.5526\) | |
| 1155.f4 | 1155m4 | \([1, 0, 0, -25445, 821730]\) | \(1821931919215868881/761147600816295\) | \(761147600816295\) | \([4]\) | \(3840\) | \(1.5526\) | |
| 1155.f1 | 1155m5 | \([1, 0, 0, -3049200, -2049655293]\) | \(3135316978843283198764801/571725\) | \(571725\) | \([2]\) | \(7680\) | \(1.8991\) | |
| 1155.f3 | 1155m6 | \([1, 0, 0, -189630, -32370975]\) | \(-754127868744065783521/15825714261328125\) | \(-15825714261328125\) | \([2]\) | \(7680\) | \(1.8991\) |
Rank
sage: E.rank()
The elliptic curves in class 1155m have rank \(0\).
Complex multiplication
The elliptic curves in class 1155m do not have complex multiplication.Modular form 1155.2.a.m
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
