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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 242760i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242760.i2 | 242760i1 | \([0, -1, 0, -126397136, 547167542940]\) | \(-9035286561666509764/3201599874375\) | \(-79133529987192723840000\) | \([2]\) | \(35389440\) | \(3.3635\) | \(\Gamma_0(N)\)-optimal |
242760.i1 | 242760i2 | \([0, -1, 0, -2022526136, 35010449795340]\) | \(18508987374528640232882/2322758025\) | \(114822619338222028800\) | \([2]\) | \(70778880\) | \(3.7101\) |
Rank
sage: E.rank()
The elliptic curves in class 242760i have rank \(1\).
Complex multiplication
The elliptic curves in class 242760i do not have complex multiplication.Modular form 242760.2.a.i
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.