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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 10920c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10920.g4 | 10920c1 | \([0, -1, 0, 9729, 398196]\) | \(6364491337435136/8034291412875\) | \(-128548662606000\) | \([2]\) | \(46080\) | \(1.3933\) | \(\Gamma_0(N)\)-optimal |
10920.g3 | 10920c2 | \([0, -1, 0, -58716, 3902580]\) | \(87450143958975184/25164018140625\) | \(6441988644000000\) | \([2, 2]\) | \(92160\) | \(1.7399\) | |
10920.g2 | 10920c3 | \([0, -1, 0, -351216, -76944420]\) | \(4678944235881273796/202428825314625\) | \(207287117122176000\) | \([2]\) | \(184320\) | \(2.0864\) | |
10920.g1 | 10920c4 | \([0, -1, 0, -861336, 307935036]\) | \(69014771940559650916/9797607421875\) | \(10032750000000000\) | \([2]\) | \(184320\) | \(2.0864\) |
Rank
sage: E.rank()
The elliptic curves in class 10920c have rank \(0\).
Complex multiplication
The elliptic curves in class 10920c do not have complex multiplication.Modular form 10920.2.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 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.