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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 30030.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30030.b1 | 30030c4 | \([1, 1, 0, -216443, -38848467]\) | \(1121392072927430144569/1425807342960\) | \(1425807342960\) | \([2]\) | \(163840\) | \(1.6103\) | |
| 30030.b2 | 30030c2 | \([1, 1, 0, -13643, -600387]\) | \(280868533884397369/9753878534400\) | \(9753878534400\) | \([2, 2]\) | \(81920\) | \(1.2638\) | |
| 30030.b3 | 30030c1 | \([1, 1, 0, -2123, 23997]\) | \(1058993490188089/345392087040\) | \(345392087040\) | \([2]\) | \(40960\) | \(0.91719\) | \(\Gamma_0(N)\)-optimal |
| 30030.b4 | 30030c3 | \([1, 1, 0, 4837, -2082483]\) | \(12511566144938951/1884337965510000\) | \(-1884337965510000\) | \([2]\) | \(163840\) | \(1.6103\) |
Rank
sage: E.rank()
The elliptic curves in class 30030.b have rank \(1\).
Complex multiplication
The elliptic curves in class 30030.b do not have complex multiplication.Modular form 30030.2.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 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.
