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SageMath
E = EllipticCurve("ev1")
E.isogeny_class()
Elliptic curves in class 243360.ev
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.ev1 | 243360ev2 | \([0, 0, 0, -58812, 4991584]\) | \(42144192/4225\) | \(2255332297420800\) | \([2]\) | \(1032192\) | \(1.6823\) | |
| 243360.ev2 | 243360ev1 | \([0, 0, 0, 4563, 377884]\) | \(1259712/8125\) | \(-67768398360000\) | \([2]\) | \(516096\) | \(1.3357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 243360.ev have rank \(0\).
Complex multiplication
The elliptic curves in class 243360.ev do not have complex multiplication.Modular form 243360.2.a.ev
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.
