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SageMath
E = EllipticCurve("ht1")
E.isogeny_class()
Elliptic curves in class 129360.ht
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.ht1 | 129360hx2 | \([0, 1, 0, -5295005, -4691413497]\) | \(227040091070464/4492125\) | \(324842016746016000\) | \([]\) | \(3919104\) | \(2.4816\) | |
| 129360.ht2 | 129360hx1 | \([0, 1, 0, -108845, 3098535]\) | \(1972117504/1082565\) | \(78284241391023360\) | \([]\) | \(1306368\) | \(1.9323\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129360.ht have rank \(0\).
Complex multiplication
The elliptic curves in class 129360.ht do not have complex multiplication.Modular form 129360.2.a.ht
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.
