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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 110946.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110946.g1 | 110946h3 | \([1, 1, 0, -135355, -19150307]\) | \(57736239625/255552\) | \(1213898638996032\) | \([2]\) | \(829440\) | \(1.7467\) | |
110946.g2 | 110946h4 | \([1, 1, 0, -68115, -38098539]\) | \(-7357983625/127552392\) | \(-605887158188894472\) | \([2]\) | \(1658880\) | \(2.0933\) | |
110946.g3 | 110946h1 | \([1, 1, 0, -9280, 320716]\) | \(18609625/1188\) | \(5643123838308\) | \([2]\) | \(276480\) | \(1.1974\) | \(\Gamma_0(N)\)-optimal |
110946.g4 | 110946h2 | \([1, 1, 0, 7530, 1373022]\) | \(9938375/176418\) | \(-838003889988738\) | \([2]\) | \(552960\) | \(1.5440\) |
Rank
sage: E.rank()
The elliptic curves in class 110946.g have rank \(0\).
Complex multiplication
The elliptic curves in class 110946.g do not have complex multiplication.Modular form 110946.2.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 LMFDB 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 LMFDB labels.