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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 29232s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29232.n1 | 29232s1 | \([0, 0, 0, -4275, -109198]\) | \(-78128296875/1365784\) | \(-151044784128\) | \([]\) | \(20736\) | \(0.94258\) | \(\Gamma_0(N)\)-optimal |
| 29232.n2 | 29232s2 | \([0, 0, 0, 16605, -521694]\) | \(6280426125/5092864\) | \(-410594681290752\) | \([]\) | \(62208\) | \(1.4919\) |
Rank
sage: E.rank()
The elliptic curves in class 29232s have rank \(1\).
Complex multiplication
The elliptic curves in class 29232s do not have complex multiplication.Modular form 29232.2.a.s
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 Cremona 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 Cremona labels.
