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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 213444.ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 213444.ea1 | 213444eh1 | \([0, 0, 0, -409101, 104546057]\) | \(-84098304/3773\) | \(-339715140512744304\) | \([]\) | \(3317760\) | \(2.1284\) | \(\Gamma_0(N)\)-optimal |
| 213444.ea2 | 213444eh2 | \([0, 0, 0, 2081079, 283506993]\) | \(15185664/9317\) | \(-611549649581401271664\) | \([]\) | \(9953280\) | \(2.6777\) |
Rank
sage: E.rank()
The elliptic curves in class 213444.ea have rank \(0\).
Complex multiplication
The elliptic curves in class 213444.ea do not have complex multiplication.Modular form 213444.2.a.ea
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.
