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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 133200.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
133200.p1 | 133200ef2 | \([0, 0, 0, -5475, 137250]\) | \(10503459/1369\) | \(2365632000000\) | \([2]\) | \(262144\) | \(1.1027\) | |
133200.p2 | 133200ef1 | \([0, 0, 0, 525, 11250]\) | \(9261/37\) | \(-63936000000\) | \([2]\) | \(131072\) | \(0.75612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 133200.p have rank \(1\).
Complex multiplication
The elliptic curves in class 133200.p do not have complex multiplication.Modular form 133200.2.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.