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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 12696.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12696.a1 | 12696i2 | \([0, -1, 0, -29800, 1843996]\) | \(19307236/1587\) | \(240571346783232\) | \([2]\) | \(67584\) | \(1.5020\) | |
12696.a2 | 12696i1 | \([0, -1, 0, 1940, 130036]\) | \(21296/207\) | \(-7844717829888\) | \([2]\) | \(33792\) | \(1.1554\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12696.a have rank \(0\).
Complex multiplication
The elliptic curves in class 12696.a do not have complex multiplication.Modular form 12696.2.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.