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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 30960.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30960.bd1 | 30960q4 | \([0, 0, 0, -2338347, 1376268986]\) | \(947094050118111698/20769216075\) | \(31008273446246400\) | \([4]\) | \(655360\) | \(2.2801\) | |
| 30960.bd2 | 30960q2 | \([0, 0, 0, -151347, 19891586]\) | \(513591322675396/68238500625\) | \(50939767762560000\) | \([2, 2]\) | \(327680\) | \(1.9336\) | |
| 30960.bd3 | 30960q1 | \([0, 0, 0, -38847, -2630914]\) | \(34739908901584/4081640625\) | \(761732100000000\) | \([2]\) | \(163840\) | \(1.5870\) | \(\Gamma_0(N)\)-optimal |
| 30960.bd4 | 30960q3 | \([0, 0, 0, 235653, 104954186]\) | \(969360123836302/3748293231075\) | \(-5596171807649126400\) | \([2]\) | \(655360\) | \(2.2801\) |
Rank
sage: E.rank()
The elliptic curves in class 30960.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 30960.bd do not have complex multiplication.Modular form 30960.2.a.bd
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.
