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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 70560.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
70560.k1 | 70560ba1 | \([0, 0, 0, -2793, -56252]\) | \(438976/5\) | \(27445158720\) | \([2]\) | \(69120\) | \(0.81622\) | \(\Gamma_0(N)\)-optimal |
70560.k2 | 70560ba2 | \([0, 0, 0, -588, -142688]\) | \(-64/25\) | \(-8782450790400\) | \([2]\) | \(138240\) | \(1.1628\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.k have rank \(1\).
Complex multiplication
The elliptic curves in class 70560.k do not have complex multiplication.Modular form 70560.2.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.