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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1440.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1440.j1 | 1440l2 | \([0, 0, 0, -732, -7616]\) | \(14526784/15\) | \(44789760\) | \([2]\) | \(512\) | \(0.38604\) | |
1440.j2 | 1440l3 | \([0, 0, 0, -507, 4354]\) | \(38614472/405\) | \(151165440\) | \([2]\) | \(512\) | \(0.38604\) | |
1440.j3 | 1440l1 | \([0, 0, 0, -57, -56]\) | \(438976/225\) | \(10497600\) | \([2, 2]\) | \(256\) | \(0.039465\) | \(\Gamma_0(N)\)-optimal |
1440.j4 | 1440l4 | \([0, 0, 0, 213, -434]\) | \(2863288/1875\) | \(-699840000\) | \([4]\) | \(512\) | \(0.38604\) |
Rank
sage: E.rank()
The elliptic curves in class 1440.j have rank \(0\).
Complex multiplication
The elliptic curves in class 1440.j do not have complex multiplication.Modular form 1440.2.a.j
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.