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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 10304.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10304.g1 | 10304u2 | \([0, 1, 0, -67873, -1014945]\) | \(263822189935250/149429406721\) | \(19586011197734912\) | \([2]\) | \(61440\) | \(1.8161\) | |
| 10304.g2 | 10304u1 | \([0, 1, 0, 16767, -117761]\) | \(7953970437500/4703287687\) | \(-308234661855232\) | \([2]\) | \(30720\) | \(1.4695\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10304.g have rank \(0\).
Complex multiplication
The elliptic curves in class 10304.g do not have complex multiplication.Modular form 10304.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
