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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 300080.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 300080.d1 | 300080d2 | \([0, 1, 0, -2063816, -1141867916]\) | \(133974081659809/192200\) | \(1394663523123200\) | \([2]\) | \(3225600\) | \(2.1770\) | |
| 300080.d2 | 300080d1 | \([0, 1, 0, -127816, -18213516]\) | \(-31824875809/1240000\) | \(-8997829181440000\) | \([2]\) | \(1612800\) | \(1.8305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 300080.d have rank \(0\).
Complex multiplication
The elliptic curves in class 300080.d do not have complex multiplication.Modular form 300080.2.a.d
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.
