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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 170352e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 170352.t2 | 170352e1 | \([0, 0, 0, -178464, 29070704]\) | \(-43614208/91\) | \(-1311562474500096\) | \([]\) | \(1161216\) | \(1.7864\) | \(\Gamma_0(N)\)-optimal |
| 170352.t3 | 170352e2 | \([0, 0, 0, 308256, 144228656]\) | \(224755712/753571\) | \(-10861048851335294976\) | \([]\) | \(3483648\) | \(2.3357\) | |
| 170352.t1 | 170352e3 | \([0, 0, 0, -2855424, -4577247376]\) | \(-178643795968/524596891\) | \(-7560896664560627920896\) | \([]\) | \(10450944\) | \(2.8850\) |
Rank
sage: E.rank()
The elliptic curves in class 170352e have rank \(0\).
Complex multiplication
The elliptic curves in class 170352e do not have complex multiplication.Modular form 170352.2.a.e
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
