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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 810.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
810.c1 | 810a1 | \([1, -1, 0, -9, 15]\) | \(-1058841/250\) | \(-20250\) | \([3]\) | \(72\) | \(-0.45459\) | \(\Gamma_0(N)\)-optimal |
810.c2 | 810a2 | \([1, -1, 0, 66, -100]\) | \(59319/40\) | \(-21257640\) | \([]\) | \(216\) | \(0.094717\) |
Rank
sage: E.rank()
The elliptic curves in class 810.c have rank \(0\).
Complex multiplication
The elliptic curves in class 810.c do not have complex multiplication.Modular form 810.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.