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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 22540.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22540.e1 | 22540f1 | \([0, -1, 0, -129007706, -563947245119]\) | \(-126142795384287538429696/9315359375\) | \(-17535083441750000\) | \([]\) | \(1700352\) | \(3.0132\) | \(\Gamma_0(N)\)-optimal |
| 22540.e2 | 22540f2 | \([0, -1, 0, -127709206, -575856798019]\) | \(-122372013839654770813696/5297595236711512175\) | \(-9972108512061963134025200\) | \([]\) | \(5101056\) | \(3.5625\) |
Rank
sage: E.rank()
The elliptic curves in class 22540.e have rank \(1\).
Complex multiplication
The elliptic curves in class 22540.e do not have complex multiplication.Modular form 22540.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
