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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 134096.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 134096.j1 | 134096h2 | \([0, -1, 0, -2104016, 1183352512]\) | \(-10418796526321/82044596\) | \(-8111542669423099904\) | \([]\) | \(1996800\) | \(2.4569\) | |
| 134096.j2 | 134096h1 | \([0, -1, 0, 23024, -2241088]\) | \(13651919/29696\) | \(-2935968764002304\) | \([]\) | \(399360\) | \(1.6522\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 134096.j have rank \(1\).
Complex multiplication
The elliptic curves in class 134096.j do not have complex multiplication.Modular form 134096.2.a.j
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.
