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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 15925m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15925.k2 | 15925m1 | \([0, 1, 1, -8983, -331306]\) | \(-43614208/91\) | \(-167282171875\) | \([]\) | \(20736\) | \(1.0392\) | \(\Gamma_0(N)\)-optimal |
| 15925.k3 | 15925m2 | \([0, 1, 1, 15517, -1623681]\) | \(224755712/753571\) | \(-1385263665296875\) | \([]\) | \(62208\) | \(1.5885\) | |
| 15925.k1 | 15925m3 | \([0, 1, 1, -143733, 51645444]\) | \(-178643795968/524596891\) | \(-964348431707171875\) | \([]\) | \(186624\) | \(2.1378\) |
Rank
sage: E.rank()
The elliptic curves in class 15925m have rank \(1\).
Complex multiplication
The elliptic curves in class 15925m do not have complex multiplication.Modular form 15925.2.a.m
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.
