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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 485100.iz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485100.iz1 | 485100iz1 | \([0, 0, 0, -378907200, 2838881989125]\) | \(10392086293512192/1684375\) | \(975120592900781250000\) | \([2]\) | \(86261760\) | \(3.4294\) | \(\Gamma_0(N)\)-optimal |
| 485100.iz2 | 485100iz2 | \([0, 0, 0, -377749575, 2857090272750]\) | \(-643570518871152/8271484375\) | \(-76616618013632812500000000\) | \([2]\) | \(172523520\) | \(3.7759\) |
Rank
sage: E.rank()
The elliptic curves in class 485100.iz have rank \(0\).
Complex multiplication
The elliptic curves in class 485100.iz do not have complex multiplication.Modular form 485100.2.a.iz
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.
