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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 61200.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61200.v1 | 61200hl2 | \([0, 0, 0, -61635, -5815550]\) | \(69375867029/1003833\) | \(374678659584000\) | \([2]\) | \(327680\) | \(1.6003\) | |
61200.v2 | 61200hl1 | \([0, 0, 0, -435, -246350]\) | \(-24389/70227\) | \(-26212087296000\) | \([2]\) | \(163840\) | \(1.2537\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61200.v have rank \(1\).
Complex multiplication
The elliptic curves in class 61200.v do not have complex multiplication.Modular form 61200.2.a.v
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.