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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 102850.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102850.z1 | 102850d1 | \([1, -1, 0, -97367, 1360541]\) | \(3687953625/2106368\) | \(58305615632000000\) | \([2]\) | \(691200\) | \(1.9068\) | \(\Gamma_0(N)\)-optimal |
| 102850.z2 | 102850d2 | \([1, -1, 0, 386633, 10556541]\) | \(230910510375/135399968\) | \(-3747957854844500000\) | \([2]\) | \(1382400\) | \(2.2534\) |
Rank
sage: E.rank()
The elliptic curves in class 102850.z have rank \(0\).
Complex multiplication
The elliptic curves in class 102850.z do not have complex multiplication.Modular form 102850.2.a.z
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.
