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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 286650.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.l1 | 286650l3 | \([1, -1, 0, -5066217, -4387819059]\) | \(-10730978619193/6656\) | \(-8919676584000000\) | \([]\) | \(7348320\) | \(2.3814\) | |
| 286650.l2 | 286650l2 | \([1, -1, 0, -49842, -8523684]\) | \(-10218313/17576\) | \(-23553520979625000\) | \([]\) | \(2449440\) | \(1.8321\) | |
| 286650.l3 | 286650l1 | \([1, -1, 0, 5283, 241191]\) | \(12167/26\) | \(-34842486656250\) | \([]\) | \(816480\) | \(1.2828\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286650.l have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.l do not have complex multiplication.Modular form 286650.2.a.l
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
