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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 372810.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372810.i1 | 372810i2 | \([1, 1, 0, -68643, -6729723]\) | \(1481933914201/53916840\) | \(1301421445761960\) | \([2]\) | \(2838528\) | \(1.6699\) | |
372810.i2 | 372810i1 | \([1, 1, 0, -10843, 287197]\) | \(5841725401/1857600\) | \(44837948174400\) | \([2]\) | \(1419264\) | \(1.3233\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 372810.i have rank \(1\).
Complex multiplication
The elliptic curves in class 372810.i do not have complex multiplication.Modular form 372810.2.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 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.