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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 207025.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 207025.bj1 | 207025bj3 | \([0, 1, 1, -24290933, 113562204669]\) | \(-178643795968/524596891\) | \(-4654725689300062570796875\) | \([]\) | \(31352832\) | \(3.4203\) | |
| 207025.bj2 | 207025bj1 | \([0, 1, 1, -1518183, -721806081]\) | \(-43614208/91\) | \(-807439092745796875\) | \([]\) | \(3483648\) | \(2.3216\) | \(\Gamma_0(N)\)-optimal |
| 207025.bj3 | 207025bj2 | \([0, 1, 1, 2622317, -3577715956]\) | \(224755712/753571\) | \(-6686403127027943921875\) | \([]\) | \(10450944\) | \(2.8709\) |
Rank
sage: E.rank()
The elliptic curves in class 207025.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 207025.bj do not have complex multiplication.Modular form 207025.2.a.bj
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.
