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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 17160t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.n4 | 17160t1 | \([0, -1, 0, -9295, 348040]\) | \(5551350318708736/27885\) | \(446160\) | \([4]\) | \(10240\) | \(0.70380\) | \(\Gamma_0(N)\)-optimal |
| 17160.n3 | 17160t2 | \([0, -1, 0, -9300, 347652]\) | \(347519589019216/777573225\) | \(199058745600\) | \([2, 4]\) | \(20480\) | \(1.0504\) | |
| 17160.n2 | 17160t3 | \([0, -1, 0, -12680, 75900]\) | \(220199214811684/125262905625\) | \(128269215360000\) | \([2, 2]\) | \(40960\) | \(1.3970\) | |
| 17160.n5 | 17160t4 | \([0, -1, 0, -6000, 594492]\) | \(-23331888216004/134595568965\) | \(-137825862620160\) | \([4]\) | \(40960\) | \(1.3970\) | |
| 17160.n1 | 17160t5 | \([0, -1, 0, -129680, -17848500]\) | \(117764966889591842/626999726925\) | \(1284095440742400\) | \([2]\) | \(81920\) | \(1.7435\) | |
| 17160.n6 | 17160t6 | \([0, -1, 0, 50240, 554092]\) | \(6847531008289918/4031426953125\) | \(-8256362400000000\) | \([2]\) | \(81920\) | \(1.7435\) |
Rank
sage: E.rank()
The elliptic curves in class 17160t have rank \(0\).
Complex multiplication
The elliptic curves in class 17160t do not have complex multiplication.Modular form 17160.2.a.t
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.
