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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 56350c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56350.r2 | 56350c1 | \([1, -1, 0, -149417, 22225741]\) | \(68835304542087/150732800\) | \(807833600000000\) | \([2]\) | \(387072\) | \(1.7437\) | \(\Gamma_0(N)\)-optimal |
| 56350.r1 | 56350c2 | \([1, -1, 0, -2389417, 1422225741]\) | \(281504613025066887/1354240\) | \(7257880000000\) | \([2]\) | \(774144\) | \(2.0903\) |
Rank
sage: E.rank()
The elliptic curves in class 56350c have rank \(0\).
Complex multiplication
The elliptic curves in class 56350c do not have complex multiplication.Modular form 56350.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
