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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 832.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 832.d1 | 832c3 | \([0, -1, 0, -29409, -1931423]\) | \(-10730978619193/6656\) | \(-1744830464\) | \([]\) | \(1152\) | \(1.0941\) | |
| 832.d2 | 832c2 | \([0, -1, 0, -289, -3679]\) | \(-10218313/17576\) | \(-4607442944\) | \([]\) | \(384\) | \(0.54480\) | |
| 832.d3 | 832c1 | \([0, -1, 0, 31, 97]\) | \(12167/26\) | \(-6815744\) | \([]\) | \(128\) | \(-0.0045051\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 832.d have rank \(1\).
Complex multiplication
The elliptic curves in class 832.d do not have complex multiplication.Modular form 832.2.a.d
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
