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SageMath
E = EllipticCurve("id1")
E.isogeny_class()
Elliptic curves in class 176400.id
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.id1 | 176400fd3 | \([0, 0, 0, -19848675, 34034089250]\) | \(157551496201/13125\) | \(72043541640000000000\) | \([2]\) | \(9437184\) | \(2.8542\) | |
| 176400.id2 | 176400fd2 | \([0, 0, 0, -1326675, 453703250]\) | \(47045881/11025\) | \(60516574977600000000\) | \([2, 2]\) | \(4718592\) | \(2.5076\) | |
| 176400.id3 | 176400fd1 | \([0, 0, 0, -444675, -108130750]\) | \(1771561/105\) | \(576348333120000000\) | \([2]\) | \(2359296\) | \(2.1610\) | \(\Gamma_0(N)\)-optimal |
| 176400.id4 | 176400fd4 | \([0, 0, 0, 3083325, 2830693250]\) | \(590589719/972405\) | \(-5337561913024320000000\) | \([2]\) | \(9437184\) | \(2.8542\) |
Rank
sage: E.rank()
The elliptic curves in class 176400.id have rank \(2\).
Complex multiplication
The elliptic curves in class 176400.id do not have complex multiplication.Modular form 176400.2.a.id
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.
