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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 88725.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88725.k1 | 88725m2 | \([1, 1, 1, -35188, -394594]\) | \(140364780373/79413075\) | \(2726101965234375\) | \([2]\) | \(580608\) | \(1.6518\) | |
88725.k2 | 88725m1 | \([1, 1, 1, 8687, -43594]\) | \(2111932187/1250235\) | \(-42918223359375\) | \([2]\) | \(290304\) | \(1.3052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88725.k have rank \(0\).
Complex multiplication
The elliptic curves in class 88725.k do not have complex multiplication.Modular form 88725.2.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 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.