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SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 102960.ef
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.ef1 | 102960m2 | \([0, 0, 0, -193587, 32784034]\) | \(29019408786852012/511225\) | \(14134348800\) | \([2]\) | \(262144\) | \(1.4876\) | |
| 102960.ef2 | 102960m1 | \([0, 0, 0, -12087, 513334]\) | \(-28253714280048/118958125\) | \(-822238560000\) | \([2]\) | \(131072\) | \(1.1410\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.ef have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.ef do not have complex multiplication.Modular form 102960.2.a.ef
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.
