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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 277200.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.v1 | 277200v1 | \([0, 0, 0, -390, -1825]\) | \(4499456/1617\) | \(2357586000\) | \([2]\) | \(106496\) | \(0.49917\) | \(\Gamma_0(N)\)-optimal |
277200.v2 | 277200v2 | \([0, 0, 0, 1185, -12850]\) | \(7888624/7623\) | \(-177829344000\) | \([2]\) | \(212992\) | \(0.84574\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.v have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.v do not have complex multiplication.Modular form 277200.2.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.