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SageMath
E = EllipticCurve("kd1")
E.isogeny_class()
Elliptic curves in class 141120.kd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.kd1 | 141120fw2 | \([0, 0, 0, -5626572, 5137025936]\) | \(68971442301/400\) | \(114247324296806400\) | \([2]\) | \(2752512\) | \(2.4633\) | |
141120.kd2 | 141120fw1 | \([0, 0, 0, -358092, 77177744]\) | \(17779581/1280\) | \(365591437749780480\) | \([2]\) | \(1376256\) | \(2.1167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.kd have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.kd do not have complex multiplication.Modular form 141120.2.a.kd
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.