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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 17160.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.d1 | 17160o2 | \([0, -1, 0, -555376, 46600060]\) | \(18500602077383458756/9797502159534375\) | \(10032642211363200000\) | \([2]\) | \(460800\) | \(2.3375\) | |
| 17160.d2 | 17160o1 | \([0, -1, 0, 132124, 5625060]\) | \(996381372425164976/630843662109375\) | \(-161495977500000000\) | \([2]\) | \(230400\) | \(1.9909\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17160.d have rank \(1\).
Complex multiplication
The elliptic curves in class 17160.d do not have complex multiplication.Modular form 17160.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
