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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 380880f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380880.f1 | 380880f1 | \([0, 0, 0, -3243, -72358]\) | \(-2387929/50\) | \(-78979276800\) | \([]\) | \(414720\) | \(0.88189\) | \(\Gamma_0(N)\)-optimal |
380880.f2 | 380880f2 | \([0, 0, 0, 13317, -327382]\) | \(165348311/125000\) | \(-197448192000000\) | \([]\) | \(1244160\) | \(1.4312\) |
Rank
sage: E.rank()
The elliptic curves in class 380880f have rank \(0\).
Complex multiplication
The elliptic curves in class 380880f do not have complex multiplication.Modular form 380880.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.