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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 32340k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32340.l2 | 32340k1 | \([0, -1, 0, -4033745, 4282003650]\) | \(-3856034557002072064/1973796785296875\) | \(-3715443487894272750000\) | \([2]\) | \(1935360\) | \(2.8436\) | \(\Gamma_0(N)\)-optimal |
| 32340.l1 | 32340k2 | \([0, -1, 0, -71010620, 230315561400]\) | \(1314817350433665559504/190690249278375\) | \(5743236387161994336000\) | \([2]\) | \(3870720\) | \(3.1901\) |
Rank
sage: E.rank()
The elliptic curves in class 32340k have rank \(0\).
Complex multiplication
The elliptic curves in class 32340k do not have complex multiplication.Modular form 32340.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
