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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 32340.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32340.w1 | 32340bc2 | \([0, 1, 0, -89196, -9905820]\) | \(2605772594896/108945375\) | \(3281232492384000\) | \([2]\) | \(165888\) | \(1.7421\) | |
| 32340.w2 | 32340bc1 | \([0, 1, 0, 2679, -571320]\) | \(1129201664/75796875\) | \(-142678824750000\) | \([2]\) | \(82944\) | \(1.3956\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32340.w have rank \(0\).
Complex multiplication
The elliptic curves in class 32340.w do not have complex multiplication.Modular form 32340.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
