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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 365400.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 365400.r1 | 365400r2 | \([0, 0, 0, -8047875, -8787289250]\) | \(2471097448795250/98942809\) | \(2308137848352000000\) | \([2]\) | \(10616832\) | \(2.6065\) | |
| 365400.r2 | 365400r1 | \([0, 0, 0, -478875, -151060250]\) | \(-1041220466500/242597383\) | \(-2829655875312000000\) | \([2]\) | \(5308416\) | \(2.2599\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 365400.r have rank \(1\).
Complex multiplication
The elliptic curves in class 365400.r do not have complex multiplication.Modular form 365400.2.a.r
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.
