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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 270400.ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 270400.ee1 | 270400ee2 | \([0, -1, 0, -36053, 2639467]\) | \(671088640/2197\) | \(16967198996800\) | \([]\) | \(870912\) | \(1.4039\) | |
| 270400.ee2 | 270400ee1 | \([0, -1, 0, -2253, -37493]\) | \(163840/13\) | \(100397627200\) | \([]\) | \(290304\) | \(0.85462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270400.ee have rank \(0\).
Complex multiplication
The elliptic curves in class 270400.ee do not have complex multiplication.Modular form 270400.2.a.ee
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
