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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 389205.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
389205.p1 | 389205p2 | \([1, -1, 0, -216405, 38969526]\) | \(-15590912409/78125\) | \(-5616234231328125\) | \([]\) | \(2580480\) | \(1.8694\) | |
389205.p2 | 389205p1 | \([1, -1, 0, -180, -28815]\) | \(-9/5\) | \(-359438990805\) | \([]\) | \(368640\) | \(0.89640\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 389205.p have rank \(0\).
Complex multiplication
The elliptic curves in class 389205.p do not have complex multiplication.Modular form 389205.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.