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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12880b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12880.h4 | 12880b1 | \([0, 0, 0, 22, -93]\) | \(73598976/276115\) | \(-4417840\) | \([2]\) | \(1280\) | \(-0.042077\) | \(\Gamma_0(N)\)-optimal |
| 12880.h3 | 12880b2 | \([0, 0, 0, -223, -1122]\) | \(4790692944/648025\) | \(165894400\) | \([2, 2]\) | \(2560\) | \(0.30450\) | |
| 12880.h1 | 12880b3 | \([0, 0, 0, -3443, -77758]\) | \(4407931365156/100625\) | \(103040000\) | \([2]\) | \(5120\) | \(0.65107\) | |
| 12880.h2 | 12880b4 | \([0, 0, 0, -923, 9658]\) | \(84923690436/9794435\) | \(10029501440\) | \([2]\) | \(5120\) | \(0.65107\) |
Rank
sage: E.rank()
The elliptic curves in class 12880b have rank \(0\).
Complex multiplication
The elliptic curves in class 12880b do not have complex multiplication.Modular form 12880.2.a.b
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 Cremona 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 Cremona labels.
