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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 143143.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 143143.s1 | 143143s3 | \([0, 1, 1, -2399349, 3524846199]\) | \(-178643795968/524596891\) | \(-4485820974246911758459\) | \([]\) | \(8709120\) | \(2.8415\) | |
| 143143.s2 | 143143s1 | \([0, 1, 1, -149959, -22441831]\) | \(-43614208/91\) | \(-778139778675259\) | \([]\) | \(967680\) | \(1.7429\) | \(\Gamma_0(N)\)-optimal |
| 143143.s3 | 143143s2 | \([0, 1, 1, 259021, -111006450]\) | \(224755712/753571\) | \(-6443775507209819779\) | \([]\) | \(2903040\) | \(2.2922\) |
Rank
sage: E.rank()
The elliptic curves in class 143143.s have rank \(1\).
Complex multiplication
The elliptic curves in class 143143.s do not have complex multiplication.Modular form 143143.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
