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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 277200.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.p1 | 277200p2 | \([0, 0, 0, -10575, 290250]\) | \(44851536/13475\) | \(39293100000000\) | \([2]\) | \(589824\) | \(1.3138\) | |
277200.p2 | 277200p1 | \([0, 0, 0, 1800, 30375]\) | \(3538944/4235\) | \(-771828750000\) | \([2]\) | \(294912\) | \(0.96721\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.p have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.p do not have complex multiplication.Modular form 277200.2.a.p
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.