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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 5824j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5824.bd2 | 5824j1 | \([0, -1, 0, -29, 71]\) | \(-43614208/91\) | \(-5824\) | \([]\) | \(576\) | \(-0.39193\) | \(\Gamma_0(N)\)-optimal |
| 5824.bd3 | 5824j2 | \([0, -1, 0, 51, 287]\) | \(224755712/753571\) | \(-48228544\) | \([]\) | \(1728\) | \(0.15737\) | |
| 5824.bd1 | 5824j3 | \([0, -1, 0, -469, -9489]\) | \(-178643795968/524596891\) | \(-33574201024\) | \([]\) | \(5184\) | \(0.70668\) |
Rank
sage: E.rank()
The elliptic curves in class 5824j have rank \(0\).
Complex multiplication
The elliptic curves in class 5824j do not have complex multiplication.Modular form 5824.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
