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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 30960.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30960.z1 | 30960s4 | \([0, 0, 0, -5323563, -4471229862]\) | \(206956783279200843/12642726098000\) | \(1019276401815281664000\) | \([2]\) | \(1327104\) | \(2.7832\) | |
| 30960.z2 | 30960s2 | \([0, 0, 0, -5242923, -4620705958]\) | \(144118734029937784467/37867520\) | \(4187844771840\) | \([2]\) | \(442368\) | \(2.2339\) | |
| 30960.z3 | 30960s3 | \([0, 0, 0, -1003563, 300642138]\) | \(1386456968640843/318028000000\) | \(25639916027904000000\) | \([2]\) | \(663552\) | \(2.4366\) | |
| 30960.z4 | 30960s1 | \([0, 0, 0, -327723, -72179878]\) | \(35198225176082067/18035507200\) | \(1994582812262400\) | \([2]\) | \(221184\) | \(1.8873\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.z have rank \(0\).
Complex multiplication
The elliptic curves in class 30960.z do not have complex multiplication.Modular form 30960.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
