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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 75712.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75712.t1 | 75712bd2 | \([0, -1, 0, -670817, -214436639]\) | \(-156116857/2744\) | \(-586773980361261056\) | \([]\) | \(1078272\) | \(2.2068\) | |
| 75712.t2 | 75712bd1 | \([0, -1, 0, 32223, -1415519]\) | \(17303/14\) | \(-2993744797761536\) | \([]\) | \(359424\) | \(1.6574\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 75712.t have rank \(0\).
Complex multiplication
The elliptic curves in class 75712.t do not have complex multiplication.Modular form 75712.2.a.t
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
