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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 17160.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.a1 | 17160b4 | \([0, -1, 0, -25660856, 50041356300]\) | \(912446049969377120252018/17177299425\) | \(35179109222400\) | \([2]\) | \(688128\) | \(2.5873\) | |
| 17160.a2 | 17160b3 | \([0, -1, 0, -1746856, 634609900]\) | \(287849398425814280018/81784533026485575\) | \(167494723638242457600\) | \([2]\) | \(688128\) | \(2.5873\) | |
| 17160.a3 | 17160b2 | \([0, -1, 0, -1603856, 782243100]\) | \(445574312599094932036/61129333175625\) | \(62596437171840000\) | \([2, 2]\) | \(344064\) | \(2.2408\) | |
| 17160.a4 | 17160b1 | \([0, -1, 0, -91356, 14498100]\) | \(-329381898333928144/162600887109375\) | \(-41625827100000000\) | \([2]\) | \(172032\) | \(1.8942\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17160.a have rank \(0\).
Complex multiplication
The elliptic curves in class 17160.a do not have complex multiplication.Modular form 17160.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
