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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2880.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2880.i1 | 2880z3 | \([0, 0, 0, -2028, -34832]\) | \(38614472/405\) | \(9674588160\) | \([2]\) | \(2048\) | \(0.73261\) | |
2880.i2 | 2880z2 | \([0, 0, 0, -228, 448]\) | \(438976/225\) | \(671846400\) | \([2, 2]\) | \(1024\) | \(0.38604\) | |
2880.i3 | 2880z1 | \([0, 0, 0, -183, 952]\) | \(14526784/15\) | \(699840\) | \([2]\) | \(512\) | \(0.039465\) | \(\Gamma_0(N)\)-optimal |
2880.i4 | 2880z4 | \([0, 0, 0, 852, 3472]\) | \(2863288/1875\) | \(-44789760000\) | \([2]\) | \(2048\) | \(0.73261\) |
Rank
sage: E.rank()
The elliptic curves in class 2880.i have rank \(1\).
Complex multiplication
The elliptic curves in class 2880.i do not have complex multiplication.Modular form 2880.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.