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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 304920.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
304920.g1 | 304920g4 | \([0, 0, 0, -219586323, -1252437275122]\) | \(442716776803843922/69178725\) | \(182972636106259507200\) | \([2]\) | \(35389440\) | \(3.2922\) | |
304920.g2 | 304920g3 | \([0, 0, 0, -25744323, 19478570078]\) | \(713435223679922/350897206275\) | \(928097284742652529612800\) | \([2]\) | \(35389440\) | \(3.2922\) | |
304920.g3 | 304920g2 | \([0, 0, 0, -13765323, -19445992522]\) | \(218121931923844/2701400625\) | \(3572502915711058560000\) | \([2, 2]\) | \(17694720\) | \(2.9456\) | |
304920.g4 | 304920g1 | \([0, 0, 0, -152823, -788700022]\) | \(-1193895376/812109375\) | \(-268496190755100000000\) | \([2]\) | \(8847360\) | \(2.5990\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 304920.g have rank \(1\).
Complex multiplication
The elliptic curves in class 304920.g do not have complex multiplication.Modular form 304920.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.