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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 23232i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23232.s3 | 23232i1 | \([0, -1, 0, -42753, -3195135]\) | \(18609625/1188\) | \(551712055099392\) | \([2]\) | \(92160\) | \(1.5793\) | \(\Gamma_0(N)\)-optimal |
23232.s4 | 23232i2 | \([0, -1, 0, 34687, -13556607]\) | \(9938375/176418\) | \(-81929240182259712\) | \([2]\) | \(184320\) | \(1.9259\) | |
23232.s1 | 23232i3 | \([0, -1, 0, -623553, 189003201]\) | \(57736239625/255552\) | \(118679393185824768\) | \([2]\) | \(276480\) | \(2.1286\) | |
23232.s2 | 23232i4 | \([0, -1, 0, -313793, 376531905]\) | \(-7357983625/127552392\) | \(-59235852123874787328\) | \([2]\) | \(552960\) | \(2.4752\) |
Rank
sage: E.rank()
The elliptic curves in class 23232i have rank \(0\).
Complex multiplication
The elliptic curves in class 23232i do not have complex multiplication.Modular form 23232.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.