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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 145656bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145656.k4 | 145656bb1 | \([0, 0, 0, -1837981911, -30610922029270]\) | \(-152435594466395827792/1646846627220711\) | \(-7418467127470538624984706816\) | \([2]\) | \(79626240\) | \(4.1638\) | \(\Gamma_0(N)\)-optimal |
| 145656.k3 | 145656bb2 | \([0, 0, 0, -29483542731, -1948576995038410]\) | \(157304700372188331121828/18069292138401\) | \(325583323983514337224909824\) | \([2, 2]\) | \(159252480\) | \(4.5103\) | |
| 145656.k2 | 145656bb3 | \([0, 0, 0, -29559387891, -1938047760363346]\) | \(79260902459030376659234/842751810121431609\) | \(30370413354414930637009923704832\) | \([2]\) | \(318504960\) | \(4.8569\) | |
| 145656.k1 | 145656bb4 | \([0, 0, 0, -471736670691, -124708934902298434]\) | \(322159999717985454060440834/4250799\) | \(153186882740639741952\) | \([2]\) | \(318504960\) | \(4.8569\) |
Rank
sage: E.rank()
The elliptic curves in class 145656bb have rank \(1\).
Complex multiplication
The elliptic curves in class 145656bb do not have complex multiplication.Modular form 145656.2.a.bb
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.
