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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 195195g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
195195.m2 | 195195g1 | \([1, 0, 0, -471307795, 7965564475712]\) | \(-2398708456982766177166009/4290716806413221559375\) | \(-20710470497646595541785284375\) | \([2]\) | \(121927680\) | \(4.1236\) | \(\Gamma_0(N)\)-optimal |
195195.m1 | 195195g2 | \([1, 0, 0, -9517927650, 357170518850625]\) | \(19755626005315513192334488489/15002747691757998046875\) | \(72415397583306730794638671875\) | \([2]\) | \(243855360\) | \(4.4702\) |
Rank
sage: E.rank()
The elliptic curves in class 195195g have rank \(1\).
Complex multiplication
The elliptic curves in class 195195g do not have complex multiplication.Modular form 195195.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.