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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5733.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5733.f1 | 5733f3 | \([0, 0, 1, -51744, -11165765]\) | \(-178643795968/524596891\) | \(-44992640429729811\) | \([]\) | \(41472\) | \(1.8824\) | |
| 5733.f2 | 5733f1 | \([0, 0, 1, -3234, 70915]\) | \(-43614208/91\) | \(-7804717011\) | \([]\) | \(4608\) | \(0.78375\) | \(\Gamma_0(N)\)-optimal |
| 5733.f3 | 5733f2 | \([0, 0, 1, 5586, 351832]\) | \(224755712/753571\) | \(-64630861568091\) | \([]\) | \(13824\) | \(1.3331\) |
Rank
sage: E.rank()
The elliptic curves in class 5733.f have rank \(1\).
Complex multiplication
The elliptic curves in class 5733.f do not have complex multiplication.Modular form 5733.2.a.f
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.
