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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 13013.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13013.f1 | 13013k2 | \([1, 1, 1, -8707, 285046]\) | \(15124197817/1294139\) | \(6246561772451\) | \([2]\) | \(25920\) | \(1.1965\) | |
13013.f2 | 13013k1 | \([1, 1, 1, 588, 21068]\) | \(4657463/41503\) | \(-200327053927\) | \([2]\) | \(12960\) | \(0.84988\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13013.f have rank \(0\).
Complex multiplication
The elliptic curves in class 13013.f do not have complex multiplication.Modular form 13013.2.a.f
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.