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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 83400.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83400.a1 | 83400j1 | \([0, -1, 0, -31208, 2132412]\) | \(210094874500/3753\) | \(60048000000\) | \([2]\) | \(193536\) | \(1.1952\) | \(\Gamma_0(N)\)-optimal |
83400.a2 | 83400j2 | \([0, -1, 0, -30208, 2274412]\) | \(-95269531250/14085009\) | \(-450720288000000\) | \([2]\) | \(387072\) | \(1.5418\) |
Rank
sage: E.rank()
The elliptic curves in class 83400.a have rank \(0\).
Complex multiplication
The elliptic curves in class 83400.a do not have complex multiplication.Modular form 83400.2.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.