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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 79781.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79781.c1 | 79781e1 | \([1, 0, 0, -21487, -1213968]\) | \(23320116793/2873\) | \(135162816113\) | \([2]\) | \(165888\) | \(1.1592\) | \(\Gamma_0(N)\)-optimal |
79781.c2 | 79781e2 | \([1, 0, 0, -19682, -1425875]\) | \(-17923019113/8254129\) | \(-388322770692649\) | \([2]\) | \(331776\) | \(1.5058\) |
Rank
sage: E.rank()
The elliptic curves in class 79781.c have rank \(0\).
Complex multiplication
The elliptic curves in class 79781.c do not have complex multiplication.Modular form 79781.2.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.