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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 101430z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.l1 | 101430z1 | \([1, -1, 0, -6715259595, -211788189256379]\) | \(1138419279070642590770503/112678869663744000\) | \(3314762142415296745439232000\) | \([2]\) | \(108380160\) | \(4.3155\) | \(\Gamma_0(N)\)-optimal |
101430.l2 | 101430z2 | \([1, -1, 0, -6209485515, -245035855334075]\) | \(-900079102684529025934663/360857020174848000000\) | \(-10615612251613300970540544000000\) | \([2]\) | \(216760320\) | \(4.6621\) |
Rank
sage: E.rank()
The elliptic curves in class 101430z have rank \(1\).
Complex multiplication
The elliptic curves in class 101430z do not have complex multiplication.Modular form 101430.2.a.z
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.