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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 246.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
246.c1 | 246c1 | \([1, 0, 1, -453897, -117739700]\) | \(10341755683137709164937/356992303104\) | \(356992303104\) | \([2]\) | \(1680\) | \(1.7144\) | \(\Gamma_0(N)\)-optimal |
246.c2 | 246c2 | \([1, 0, 1, -453257, -118088116]\) | \(-10298071306410575356297/60769798505543808\) | \(-60769798505543808\) | \([2]\) | \(3360\) | \(2.0610\) |
Rank
sage: E.rank()
The elliptic curves in class 246.c have rank \(0\).
Complex multiplication
The elliptic curves in class 246.c do not have complex multiplication.Modular form 246.2.a.c
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.