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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 31850bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31850.cl3 | 31850bz1 | \([1, 0, 0, 587, -8933]\) | \(12167/26\) | \(-47794906250\) | \([]\) | \(27216\) | \(0.73345\) | \(\Gamma_0(N)\)-optimal |
| 31850.cl2 | 31850bz2 | \([1, 0, 0, -5538, 315692]\) | \(-10218313/17576\) | \(-32309356625000\) | \([]\) | \(81648\) | \(1.2828\) | |
| 31850.cl1 | 31850bz3 | \([1, 0, 0, -562913, 162511817]\) | \(-10730978619193/6656\) | \(-12235496000000\) | \([]\) | \(244944\) | \(1.8321\) |
Rank
sage: E.rank()
The elliptic curves in class 31850bz have rank \(0\).
Complex multiplication
The elliptic curves in class 31850bz do not have complex multiplication.Modular form 31850.2.a.bz
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.
