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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 285940.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
285940.f1 | 285940f1 | \([0, 0, 0, -23548, 1390173]\) | \(151732224/85\) | \(808959716560\) | \([2]\) | \(580608\) | \(1.2321\) | \(\Gamma_0(N)\)-optimal |
285940.f2 | 285940f2 | \([0, 0, 0, -19343, 1902342]\) | \(-5256144/7225\) | \(-1100185214521600\) | \([2]\) | \(1161216\) | \(1.5787\) |
Rank
sage: E.rank()
The elliptic curves in class 285940.f have rank \(2\).
Complex multiplication
The elliptic curves in class 285940.f do not have complex multiplication.Modular form 285940.2.a.f
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.