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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1248.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1248.j1 | 1248c1 | \([0, 1, 0, -2902, -61132]\) | \(42246001231552/14414517\) | \(922529088\) | \([2]\) | \(768\) | \(0.69180\) | \(\Gamma_0(N)\)-optimal |
1248.j2 | 1248c2 | \([0, 1, 0, -2497, -78385]\) | \(-420526439488/390971529\) | \(-1601419382784\) | \([2]\) | \(1536\) | \(1.0384\) |
Rank
sage: E.rank()
The elliptic curves in class 1248.j have rank \(0\).
Complex multiplication
The elliptic curves in class 1248.j do not have complex multiplication.Modular form 1248.2.a.j
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.