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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 235200k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.k2 | 235200k1 | \([0, -1, 0, 1919167, 82569537]\) | \(2595575/1512\) | \(-455386337280000000000\) | \([]\) | \(9953280\) | \(2.6534\) | \(\Gamma_0(N)\)-optimal |
| 235200.k1 | 235200k2 | \([0, -1, 0, -27480833, 58676769537]\) | \(-7620530425/526848\) | \(-158676839301120000000000\) | \([]\) | \(29859840\) | \(3.2027\) |
Rank
sage: E.rank()
The elliptic curves in class 235200k have rank \(0\).
Complex multiplication
The elliptic curves in class 235200k do not have complex multiplication.Modular form 235200.2.a.k
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.
