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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 6084.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6084.o1 | 6084l2 | \([0, 0, 0, -797511, 274128478]\) | \(-368484688\) | \(-152234930075904\) | \([3]\) | \(56160\) | \(1.9552\) | |
| 6084.o2 | 6084l1 | \([0, 0, 0, -6591, 628342]\) | \(-208\) | \(-152234930075904\) | \([]\) | \(18720\) | \(1.4059\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6084.o have rank \(1\).
Complex multiplication
The elliptic curves in class 6084.o do not have complex multiplication.Modular form 6084.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
