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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 235340c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235340.c2 | 235340c1 | \([0, 1, 0, 22974, -50332751]\) | \(10496/8575\) | \(-1095531741435401200\) | \([3]\) | \(2851632\) | \(2.1405\) | \(\Gamma_0(N)\)-optimal |
235340.c1 | 235340c2 | \([0, 1, 0, -9625966, -11499764955]\) | \(-772086379264/109375\) | \(-13973619150961750000\) | \([]\) | \(8554896\) | \(2.6898\) |
Rank
sage: E.rank()
The elliptic curves in class 235340c have rank \(0\).
Complex multiplication
The elliptic curves in class 235340c do not have complex multiplication.Modular form 235340.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.