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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 450800cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450800.cs1 | 450800cs1 | \([0, -1, 0, -3225192658, 70499856025187]\) | \(-126142795384287538429696/9315359375\) | \(-273985678777343750000\) | \([]\) | \(163233792\) | \(3.8179\) | \(\Gamma_0(N)\)-optimal |
| 450800.cs2 | 450800cs2 | \([0, -1, 0, -3192730158, 71988485212687]\) | \(-122372013839654770813696/5297595236711512175\) | \(-155814195500968173969143750000\) | \([]\) | \(489701376\) | \(4.3672\) |
Rank
sage: E.rank()
The elliptic curves in class 450800cs have rank \(1\).
Complex multiplication
The elliptic curves in class 450800cs do not have complex multiplication.Modular form 450800.2.a.cs
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
