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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 94192.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94192.e1 | 94192s2 | \([0, -1, 0, -28934885, 59923843021]\) | \(-1099616058781696/143578043\) | \(-349813016002317529088\) | \([]\) | \(8064000\) | \(2.9624\) | |
| 94192.e2 | 94192s1 | \([0, -1, 0, 264635, 1718381]\) | \(841232384/487403\) | \(-1187506876929486848\) | \([]\) | \(1612800\) | \(2.1577\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94192.e have rank \(0\).
Complex multiplication
The elliptic curves in class 94192.e do not have complex multiplication.Modular form 94192.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
