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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 37905.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37905.g1 | 37905k4 | \([1, 1, 1, -40620, 3133920]\) | \(157551496201/13125\) | \(617477188125\) | \([2]\) | \(96768\) | \(1.3063\) | |
37905.g2 | 37905k2 | \([1, 1, 1, -2715, 40872]\) | \(47045881/11025\) | \(518680838025\) | \([2, 2]\) | \(48384\) | \(0.95968\) | |
37905.g3 | 37905k1 | \([1, 1, 1, -910, -10390]\) | \(1771561/105\) | \(4939817505\) | \([2]\) | \(24192\) | \(0.61311\) | \(\Gamma_0(N)\)-optimal |
37905.g4 | 37905k3 | \([1, 1, 1, 6310, 264692]\) | \(590589719/972405\) | \(-45747649913805\) | \([2]\) | \(96768\) | \(1.3063\) |
Rank
sage: E.rank()
The elliptic curves in class 37905.g have rank \(0\).
Complex multiplication
The elliptic curves in class 37905.g do not have complex multiplication.Modular form 37905.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.