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SageMath
E = EllipticCurve("mf1")
E.isogeny_class()
Elliptic curves in class 435600mf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435600.mf2 | 435600mf1 | \([0, 0, 0, -1155, 7810]\) | \(18865/8\) | \(72260812800\) | \([]\) | \(331776\) | \(0.78034\) | \(\Gamma_0(N)\)-optimal* |
435600.mf1 | 435600mf2 | \([0, 0, 0, -80355, 8767330]\) | \(6352571665/2\) | \(18065203200\) | \([]\) | \(995328\) | \(1.3297\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435600mf have rank \(0\).
Complex multiplication
The elliptic curves in class 435600mf do not have complex multiplication.Modular form 435600.2.a.mf
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.