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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 57960.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57960.a1 | 57960bf2 | \([0, 0, 0, -310203, -66480202]\) | \(59699126465470854/19845765625\) | \(1097391456000000\) | \([2]\) | \(319488\) | \(1.8589\) | |
57960.a2 | 57960bf1 | \([0, 0, 0, -22083, -731218]\) | \(43075884983148/16573802875\) | \(458232501888000\) | \([2]\) | \(159744\) | \(1.5123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 57960.a have rank \(0\).
Complex multiplication
The elliptic curves in class 57960.a do not have complex multiplication.Modular form 57960.2.a.a
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.