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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 96.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96.a1 | 96b2 | \([0, -1, 0, -32, -60]\) | \(7301384/3\) | \(1536\) | \([2]\) | \(8\) | \(-0.42622\) | |
96.a2 | 96b3 | \([0, -1, 0, -17, 33]\) | \(140608/3\) | \(12288\) | \([4]\) | \(8\) | \(-0.42622\) | |
96.a3 | 96b1 | \([0, -1, 0, -2, 0]\) | \(21952/9\) | \(576\) | \([2, 2]\) | \(4\) | \(-0.77279\) | \(\Gamma_0(N)\)-optimal |
96.a4 | 96b4 | \([0, -1, 0, 8, -8]\) | \(97336/81\) | \(-41472\) | \([2]\) | \(8\) | \(-0.42622\) |
Rank
sage: E.rank()
The elliptic curves in class 96.a have rank \(0\).
Complex multiplication
The elliptic curves in class 96.a do not have complex multiplication.Modular form 96.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.