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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1440.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1440.c1 | 1440j3 | \([0, 0, 0, -1443, 21098]\) | \(890277128/15\) | \(5598720\) | \([2]\) | \(512\) | \(0.42511\) | |
1440.c2 | 1440j2 | \([0, 0, 0, -363, -2338]\) | \(14172488/1875\) | \(699840000\) | \([2]\) | \(512\) | \(0.42511\) | |
1440.c3 | 1440j1 | \([0, 0, 0, -93, 308]\) | \(1906624/225\) | \(10497600\) | \([2, 2]\) | \(256\) | \(0.078535\) | \(\Gamma_0(N)\)-optimal |
1440.c4 | 1440j4 | \([0, 0, 0, 132, 1568]\) | \(85184/405\) | \(-1209323520\) | \([2]\) | \(512\) | \(0.42511\) |
Rank
sage: E.rank()
The elliptic curves in class 1440.c have rank \(1\).
Complex multiplication
The elliptic curves in class 1440.c do not have complex multiplication.Modular form 1440.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.