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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 436800.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.c1 | 436800c1 | \([0, -1, 0, -13778833, 19686535537]\) | \(9040887701683472/2380530789\) | \(76176985248000000000\) | \([2]\) | \(29491200\) | \(2.7995\) | \(\Gamma_0(N)\)-optimal |
436800.c2 | 436800c2 | \([0, -1, 0, -12088833, 24694005537]\) | \(-1526394922573748/1174052430369\) | \(-150278711087232000000000\) | \([2]\) | \(58982400\) | \(3.1461\) |
Rank
sage: E.rank()
The elliptic curves in class 436800.c have rank \(1\).
Complex multiplication
The elliptic curves in class 436800.c do not have complex multiplication.Modular form 436800.2.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.