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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 60648o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60648.bm3 | 60648o1 | \([0, 1, 0, -336572, -75268032]\) | \(350104249168/2793\) | \(33638181282048\) | \([2]\) | \(460800\) | \(1.7677\) | \(\Gamma_0(N)\)-optimal |
| 60648.bm2 | 60648o2 | \([0, 1, 0, -343792, -71877520]\) | \(93280467172/7800849\) | \(375805761283040256\) | \([2, 2]\) | \(921600\) | \(2.1142\) | |
| 60648.bm4 | 60648o3 | \([0, 1, 0, 363768, -328863312]\) | \(55251546334/517244049\) | \(-49836445649330522112\) | \([2]\) | \(1843200\) | \(2.4608\) | |
| 60648.bm1 | 60648o4 | \([0, 1, 0, -1166872, 402216560]\) | \(1823652903746/328593657\) | \(31659987117213321216\) | \([2]\) | \(1843200\) | \(2.4608\) |
Rank
sage: E.rank()
The elliptic curves in class 60648o have rank \(1\).
Complex multiplication
The elliptic curves in class 60648o do not have complex multiplication.Modular form 60648.2.a.o
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.
