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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 372810.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372810.c1 | 372810c2 | \([1, 1, 0, -344577298, 2461691961652]\) | \(920951868692595924370239353/46802812500000000000\) | \(229942217812500000000000\) | \([2]\) | \(90832896\) | \(3.5528\) | |
372810.c2 | 372810c1 | \([1, 1, 0, -22703378, 34054482228]\) | \(263419801326311610134393/50412272025600000000\) | \(247675492461772800000000\) | \([2]\) | \(45416448\) | \(3.2062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 372810.c have rank \(0\).
Complex multiplication
The elliptic curves in class 372810.c do not have complex multiplication.Modular form 372810.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.