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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 107712.eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
107712.eb1 | 107712ek2 | \([0, 0, 0, -104844, 13066000]\) | \(666940371553/37026\) | \(7075778789376\) | \([2]\) | \(294912\) | \(1.5310\) | |
107712.eb2 | 107712ek1 | \([0, 0, 0, -6924, 179728]\) | \(192100033/38148\) | \(7290196328448\) | \([2]\) | \(147456\) | \(1.1844\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 107712.eb have rank \(0\).
Complex multiplication
The elliptic curves in class 107712.eb do not have complex multiplication.Modular form 107712.2.a.eb
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.